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<image>Determine the intervals on which the functions are increasing, decreasing, or constant.
|
\text { increasing } \quad(-3,1) ; \quad \text { constant }(-\infty,-3) \cup(1, \infty)
|
mathverse_vi_2503
|
|
<image>Find the absolute maximum of the function.
|
(-1.8,10)
|
mathverse_vi_2508
|
|
<image>Write the equation for the function.
|
f(x)=|x-3|
|
mathverse_vi_2513
|
|
<image>Determine whether the graphed function is even, odd, or neither.
|
even
|
mathverse_vi_2518
|
|
<image>Write an equation for the function.
|
f(x)=\frac{1}{2}|x+2|+1
|
mathverse_vi_2523
|
|
<image>Write an equation for the function.
|
f(x)=-3|x-3|+3
|
mathverse_vi_2528
|
|
<image>Which of the following could be the equation of the graphed line?
Choices:
A.$3 x-8 y=24$
B.$3 x-8 y=-24$
C.$3 x+8 y=24$
D.$3 x+8 y=-24$
|
B
|
mathverse_vi_2533
|
|
<image>What is the slope of the line?
|
slope =-4
|
mathverse_vi_2538
|
|
<image>Write the inequality that describes the points in the shaded region.
|
$y \leq 5$
|
mathverse_vi_2543
|
|
<image>State the inequality that describes the region drawn in the number plane.
|
$y \geq-2 x-6$
|
mathverse_vi_2548
|
|
<image>State the inequality that describes the region drawn in the number plane.
|
$y<2 x+6$
|
mathverse_vi_2553
|
|
<image>State the inequality that describes the region drawn in the number plane.
|
$y>-3 x$
|
mathverse_vi_2558
|
|
<image>State the inequality that describes the region drawn in the number plane.
|
$y \leq 2 x+3$
|
mathverse_vi_2563
|
|
<image>The graph shows the temperature of a room after the heater has been turned on. What is the slope of the function?
|
Slope $=\frac{1}{5}$
|
mathverse_vi_2568
|
|
<image>The graph shows the amount of water remaining in a bucket that was initially full before a hole was made in its side. What is the slope of the function?
|
Slope $=-\frac{1}{2}$
|
mathverse_vi_2573
|
|
<image>Consider the graph of the equation $y=4^{x}$. What can we say about the $y$-value of every point on the graph?
Choices:
A.The $y$-value of most points of the graph is greater than 1.
B.The $y$-value of every point on the graph is positive.
C.The $y$-value of every point on the graph is an integer.
D.The $y$-value of most points on the graph is positive, and the $y$-value at one point is 0.
|
B
|
mathverse_vi_2578
|
|
<image>Consider the graphs of the functions $y=4^{x}$ and $y=\left(\frac{1}{4}\right)^{x}$. How would you describe the rate of increase of $y=4^{x}$ ?
Choices:
A.$y$ is increasing at a constant rate
B.$y$ is increasing at a decreasing rate
C.$y$ is increasing at an increasing rate
|
(C)
|
mathverse_vi_2583
|
|
<image>The graph of $y=2^{x}$ is displayed here. Which single option below gives us the graph's domain?
Choices:
A.$x \geq 0$
B.$x>0$
C.All real $x$
D.$x<0$
|
(C)
|
mathverse_vi_2588
|
|
<image>The function $f(x)=5 x-x^2$ gives the number of mosquitos in the forest (in millions), and the function $g(x)=3 x-0.5 x^2$ gives the number of bats (in millions). In both equations $x$ represents rainfall (in centimeters). When there is $0 \mathrm{~cm}$ of rainfall, the number of mosquitos is the same as the number of bats. What is another rainfall amount where the number of mosquitos is the same as the number of bats?
Round your answer to the nearest half centimeter.
|
4
|
mathverse_vi_2593
|
|
<image>Esteban's account balance can be modeled by $f(t)=1000 \cdot e^{(0.08 t)}$ and Anna's account balance can be modeled by $g(t)=750 \cdot e^{(0.12 t)}$, where $t$ is the number of years since they opened their accounts. When do the accounts have the same balance?
Round your answer to the nearest integer.
|
7
|
mathverse_vi_2598
|
|
<image>This is the graph of $y=x^3-x^2-x$. Use the graph to determine how many solutions the equation $x^3-x^2-x=-2$ has.
Choices:
A.No solutions
B.One solution
C.Two solutions
D.Three solutions
|
(B)
|
mathverse_vi_2603
|
|
<image>This is the graph of $y=\sqrt{6 x+7}$. Use the graph to find an approximate solution to $\sqrt{6 x+7}=6$. Round your answer to the nearest integer.
|
5
|
mathverse_vi_2608
|
|
<image>$f$ and $g$ can model the heights (in meters) of two airplanes. $t$ is the number of minutes that have passed since noon at a local airport. Which statements represent the meaning of the intersection points of the graphs?
Choices:
A.They mean that one airplane was initially higher than the other airplane.
B.They mean that the airplanes reached the same height when they were both at 10,000 meters.
C.They give the solutions to the equation $f(t)=0$.
D.They give the solutions to the equation $f(t)=g(t)$.
|
(B)
|
mathverse_vi_2613
|
|
<image>What is the value of the y-coordinate of point A?
Choices:
A:$\sin \left(0^{\circ}\right)$
B:$\cos \left(0^{\circ}\right)$
C:$\sin \left(90^{\circ}\right)$
D:$\cos \left(90^{\circ}\right)$
E:$\hline \sin \left(270^{\circ}\right)$
F:$\cos \left(270^{\circ}\right)$
|
E
|
mathverse_vi_2618
|
|
<image>Which of the coordinates is equal to \sin \left(310^{\circ}\right)?
Choices:
A:x-coordinate of point A
B:y-coordinate of point A
C:x-coordinate of point B
D:y-coordinate of point B
E:x-coordinate of point C
F:y-coordinate of point C
|
F
|
mathverse_vi_2623
|
|
<image>What is the value of the x-coordinate of point A?
Choices:
A:$\sin \left(50^{\circ}\right)$
B:$\cos \left(50^{\circ}\right)$
C:$\sin \left(140^{\circ}\right)$
D:$\cos \left(140^{\circ}\right)$
E:$\sin \left(230^{\circ}\right)$
F:$\cos \left(230^{\circ}\right)$
|
F
|
mathverse_vi_2628
|
|
<image>What is the value of the x-coordinate of point A?
Choices:
A:$\sin \left(\frac{\pi}{5}\right)$
B:$\cos \left(\frac{\pi}{5}\right)$
C:$\sin \left(\frac{6 \pi}{5}\right)$
D:$\cos \left(\frac{6 \pi}{5}\right)$
E:$\sin \left(\frac{9 \pi}{5}\right)$
F:$\cos \left(\frac{9 \pi}{5}\right)$
|
D
|
mathverse_vi_2633
|
|
<image>Which of the coordinates is equal to $\cos (\pi)$ ?
Choices:
A:$x$-coordinate of point $A$
B:$y$-coordinate of point $A$
C:$x$-coordinate of point $B$
D:$y$-coordinate of point $B$
E:$x$-coordinate of point $C$
F:$y$-coordinate of point $C$
|
E
|
mathverse_vi_2638
|
|
<image>It has an amplitude of 1.8 . What is the midline equation of the function?
|
0.2
|
mathverse_vi_2643
|
|
<image>What is the midline equation of the function?
|
-5.35
|
mathverse_vi_2648
|
|
<image>What is the midline equation of the function?
|
2
|
mathverse_vi_2653
|
|
<image>What is the midline equation of the function? Give an exact expression.
|
7.7
|
mathverse_vi_2658
|
|
<image>What is the amplitude of the function?
|
1.5
|
mathverse_vi_2663
|
|
<image>What is the amplitude of the function?
|
3.15
|
mathverse_vi_2668
|
|
<image>What is the amplitude of the function?
|
4.6
|
mathverse_vi_2673
|
|
<image>What is the amplitude of the function?
|
5.3
|
mathverse_vi_2678
|
|
<image>What is the period of the function? Give an exact value.
|
\pi
|
mathverse_vi_2683
|
|
<image>What is the period of the function? Give an exact value.
|
{8}{5} \pi
|
mathverse_vi_2688
|
|
<image>What is the period of the function? Give an exact value.
|
4 \pi
|
mathverse_vi_2693
|
|
<image>What is the period of the function? Give an exact value.
$+\stackrel{x}{=}$ units
|
14
|
mathverse_vi_2698
|
|
<image>What is the midline equation of the function?
|
3
|
mathverse_vi_2703
|
|
<image>What is the amplitude of the function?
|
6.5
|
mathverse_vi_2708
|
|
<image>Find a formula for $f(x)$. Give an exact expression.
|
3 \cos (2 \pi x+4 \pi)-6
|
mathverse_vi_2713
|
|
<image>Kai is swinging on a trapeze in a circus show. The horizontal distance between Kai and the edge of the stage, in meters, is modeled by $D(t)$ where $t$ is the time in seconds. What is the meaning of the highlighted segment?
Choices:
A:Kai completes 10 swing cycles per second.
B:The trapeze is hung $\mathbf{1 0}$ meters from the edge of the stage.
C:Kai completes a single swing cycle in 10 seconds.
D:The trapeze is $\mathbf{1 0}$ meters long.
|
C
|
mathverse_vi_2718
|
|
<image>Sia is swinging from a chandelier. The horizontal distance between Sia and the wall, in meters, is modeled by $D(t)$ where $t$ is the time in seconds. What is the meaning of the highlighted segment?
Choices:
A:The chandelier is hung 2 meters from the wall.
B:The furthest Sia gets from the point where the chandelier hangs is 2 meters.
C:The chandelier is 2 meters wide.
D:Sia completes 2 swing cycles per second.
|
B
|
mathverse_vi_2723
|
|
<image>A fly is standing on a bike wheel in motion. The vertical distance between the fly and the ground, in centimeters, is modeled by $H(t)$ where $t$ is the time in seconds. What is the meaning of the highlighted segment?
Choices:
A:The wheel completes a single cycle in 4 seconds.
B:The height of the wheel's center is 4 centimeters.
C:The radius of the wheel is 4 centimeters.
D:The bike's speed is 4 centimeters per second.
|
A
|
mathverse_vi_2728
|
|
<image>Below is the graph of $h(x)$. Give an exact expression.
|
3.5 \cos \left(\frac{2}{3} x+\frac{4 \pi}{3}\right)-0.5
|
mathverse_vi_2733
|
|
<image>Emile is observing a wind turbine. The vertical distance between the ground and the tip of one of the turbine's blades, in meters, is modeled by $H(t)$ where $t$ is the time in seconds. What is the meaning of the highlighted segment?
Choices:
A:The turbine's center is 35 meters above the ground.
B:The turbine completes a single cycle in 35 seconds.
C:The length of the blade is 35 meters.
D:The turbine has 35 blades.
|
A
|
mathverse_vi_2738
|
|
<image>There is a function $h(t)$, where $t$ corresponds to the number of hours after 12:00 a.m. According to Takoda's research, approximately how much time passes between two consecutive high tides?
|
12.5
|
mathverse_vi_2743
|
|
<image>Elena knows that Lea has a garden with an area of 100 square meters. She does not know the specific width, $w$, and length, $l$ of the garden. The graph below represents the widths that correspond to possible lengths of Lea's garden. As the possible width of Lea's garden increases, what does its possible length approach?
Choices:
A:$\infty$
B:$\hline 0$
C:$\hline 10$
D:$\hline 120$
|
B
|
mathverse_vi_2748
|
|
<image>Catalina modeled the relationship between the number of months $T$ since she opened the restaurant and its profit $P$ (in dollars, measured as income minus expenses) as
$$
P=80(T-4)^2-300 \text {. }
$$ She wanted to create a graph to show the restaurant's profits over the first year. Here is her work: What mistakes did Catalina make when drawing the graph?
Choices:
A:Inappropriate scale for $x$-axis
B:Inappropriate scale for $y$-axis
C:Wrong/missing label for $x$-axis
D:Wrong/missing label for $y$-axis
E:Catalina didn't make any mistake
|
B
|
mathverse_vi_2753
|
|
<image>Ashlynn models the relationship between the temperature $C$ of a hot cup of tea (in degrees Celsius) and time $T$ since the tea was poured into the cup (in minutes) as $C=20+20 \cdot 0.88^T$. She wanted to graph the relationship over the first half hour. Here is her work: What mistakes did Ashlynn make when drawing the graph?
Choices:
A:Inappropriate scale for $x$-axis
B:Inappropriate scale for $y$-axis
C:Wrong/missing label for $x$-axis
D:Wrong/missing label for $y$-axis
E:Ashlynn didn't make any mistake
|
E
|
mathverse_vi_2758
|
|
<image>Which of the coordinates is equal to $\sin \left(200^{\circ}\right)$ ?
Choices:
A:$x$-coordinate of point $A$
B:$y$-coordinate of point $A$
C:$x$-coordinate of point $B$
D:$y$-coordinate of point $B$
E:$x$-coordinate of point $C$
F:$y$-coordinate of point $C$
|
D
|
mathverse_vi_2763
|
|
<image>A function $p$ is graphed. What could be the equation of $p$ ?
Choices:
A:$p(x)=(x+1)^2(2 x+5)^2(x-3)^2$
B:$p(x)=(x+1)^2(2 x+5)(x-3)^2$
C:$p(x)=(x+1)^2(2 x+5)(x-3)$
D:$p(x)=(x+1)(2 x+5)(x-3)^2$
|
B
|
mathverse_vi_2768
|
|
<image>Which two of the following expressions are OPPOSITE of $\cos (\theta)$ ? Choose 2 answers:
Choices:
A:$\cos (\pi+\theta)$
B:$\cos \left(\frac{\pi}{2}-\theta\right)$
C:$\cos (\pi-\theta)$
D:$\cos (2 \pi-\theta)$
|
A
C
|
mathverse_vi_2773
|
|
<image>Evaluate the following expressions to the nearest hundredth or as an exact ratio.
|
-4.9
-4.9
|
mathverse_vi_2778
|
|
<image>10 \cdot f(7) + 9 \cdot g(-1) =
|
-1
|
mathverse_vi_2783
|
|
<image>What is the domain of h?
Choices:
A:-5 \leq x \leq 7
B:-5 \leq x \leq 4
C:-5 \leq x \leq 5
D:-5 \leq x \leq 6
|
C
|
mathverse_vi_2788
|
|
<image>What is the range of g?
Choices:
A:-4 \leq g(x) \leq 9
B:The $g(x)$-values $-5,-2,1,3$, and 4
C:The $g(x)$-values $-4,0$, and 9
D:-5 \leq g(x) \leq 4
|
A
|
mathverse_vi_2793
|
|
<image>Which of these statements are true?
Choices:
A:The largest possible number of mosquitoes is 2 million mosquitoes.
B:The largest possible number of mosquitoes is 4 million mosquitoes.
C:More rainfall always relates to less mosquitoes.
D:More rainfall relates to less mosquitoes as long as rainfall is less than $2 \mathrm{~cm}$.
|
B
|
mathverse_vi_2798
|
|
<image>Is the discriminant of g positive, zero, or negative?
Choices:
A:Positivie
B:Zero
C:Negative
|
C
|
mathverse_vi_2803
|
|
<image>Is the discriminant of f positive, zero, or negative?
Choices:
A:Positivie
B:Zero
C:Negative
|
B
|
mathverse_vi_2808
|
|
<image>Is the discriminant of g positive, zero, or negative?
Choices:
A:Positivie
B:Zero
C:Negative
|
B
|
mathverse_vi_2813
|
|
<image>f(x)=4(x-5)^2+2. Which function has a greater minimum, f(x) or g(x)?
Choices:
A:$f$ has a greater minimum than $g$.
B:$g$ has a greater minimum than $f$.
C:$f$ and $g$ share the same minimum.
|
B
|
mathverse_vi_2818
|
|
<image>f(x)=x^2+x-6. How many roots do the functions have in common, f(x) and g(x)?
Choices:
A:$f$ and $g$ share the same root(s).
B:$f$ and $g$ share one root in common but each have another root that is not shared.
C:$f$ and $g$ share no roots in common.
|
B
|
mathverse_vi_2823
|
|
<image>f(x)=x^2-2x+1. Which function has a greater y-intercept, f(x) or g(x)?
Choices:
A:$f$ has a greater $y$-intercept than $g$.
B:$g$ has a greater $y$-intercept than $f$.
C:$f$ and $g$ share the same $y$-intercept.
|
A
|
mathverse_vi_2828
|
|
<image>f(x)=4x^2-108. Do the functions have the same concavity, f(x) and g(x)?
Choices:
A:Yes, $f$ and $g$ are both concave down.
B:Yes, $f$ and $g$ are both concave up.
C:No, $f$ is concave up and $g$ is concave down.
D:No, $f$ is concave down and $g$ is concave up.
|
C
|
mathverse_vi_2833
|
|
<image>Write the equation for g(x).
|
\[g(x)=(x + 4)^2 - 5\].
|
mathverse_vi_2838
|
|
<image>Write the equation for g(x).
|
g(x)=x^2-3
|
mathverse_vi_2843
|
|
<image>Write the equation for g(x).
|
0.75 x^2
|
mathverse_vi_2848
|
|
<image>Find the equation of the dashed line. Use exact numbers.
|
g(x)=-x^2
|
mathverse_vi_2853
|
|
<image>f(x)=-5(x+4)^2+8. Which function has a greater maximum, f(x) or g(x)?
Choices:
A:$f$ has a greater maximum than $g$.
B:$g$ has a greater maximum than $f$.
C:$f$ and $g$ share the same maximum.
|
C
|
mathverse_vi_2858
|
|
<image>Write the equation for g(x).
|
g(x)=(x+2)^2+1
|
mathverse_vi_2863
|
|
<image>The function A models the rectangle's area (in square meters) as a function of its width (in meters). Which of these statements are true?
Choices:
A:Greater width always relates to smaller area.
B:Greater width relates to smaller area as long as the width is less than $10 \mathrm{~m}$.
C:When there is no width, the area is $20 \mathrm{~m}^2$.
D:When there is no width, the area is $0 \mathrm{~m}^2$.
|
D
|
mathverse_vi_2868
|
|
<image>g(x) is shown in the figure,f(x)=x^2+4x. How many roots do the functions have in common?
Choices:
A:$f$ and $g$ share the same root(s).
B:$f$ and $g$ share one root in common but each have another root that is not shared.
C:$f$ and $g$ share no roots in common.
|
C
|
mathverse_vi_2873
|
|
<image>What could be the equation of p?
Choices:
A:p(x)=(x+5)(2 x+3)(x-2)
B:p(x)=(x-5)(2 x-3)(x+2)
C:p(x)=(-5 x)\left(-\frac{3}{2} x\right)(2 x)
D:p(x)=(5 x)\left(\frac{3}{2} x\right)(-2 x)
|
A
|
mathverse_vi_2878
|
|
<image>What could be the equation of p?
Choices:
A:p(x)=x(x-3)^2(2 x+7)
B:p(x)=x^2(x-3)(2 x+7)
C:p(x)=x(x-3)^2(2 x+7)^2
D:p(x)=x(x-3)(2 x+7)^2
|
A
|
mathverse_vi_2883
|
|
<image>Peter received a lump sum payment of $\$ 50000$ for an insurance claim (and decided not to put it in a savings account).
Every month, he withdraws $5 \%$ of the remaining funds.
The funds after $x$ months is shown below.
How much would the first withdrawal be?
|
2500
|
mathverse_vi_2888
|
|
<image>In a memory study, subjects are asked to memorize some content and recall as much as they can remember each day thereafter. Each day, Maximilian finds that he has forgotten $15 \%$ of what he could recount the day before. Lucy also took part in the study. The given graphs represent the percentage of content that Maximilian (gray) and Lucy (black) could remember after $t$ days.
Which of the following could model the percentage that Lucy can still recall after $t$ days?
Choices:
A:$Q=(0.85)^{t}$
B:$Q=(0.83)^{t}$
C:$Q=(0.87)^{t}$
|
C
|
mathverse_vi_2893
|
|
<image>In a memory study, subjects are asked to memorize some content and recall as much as they can remember each day thereafter. Each day, Maximilian finds that he has forgotten $15 \%$ of what he could recount the day before. Lucy also took part in the study. The given graphs represent the percentage of content that Maximilian (gray) and Lucy (black) could remember after $t$ days.
On each day, what percentage of the previous day's content did Lucy forget?
|
$13 \%$
|
mathverse_vi_2898
|
|
<image>For function graphed below, determine if it has an inverse function.
Choices:
A:Yes
B:No
|
A
|
mathverse_vi_2903
|
|
<image>For function graphed below, determine if it has an inverse function.
Choices:
A:Yes
B:No
|
A
|
mathverse_vi_2908
|
|
<image>Do the following graph have inverse functions?
Choices:
A:Yes
B:No
|
A
|
mathverse_vi_2913
|
|
<image>Do the following graph have inverse functions?
Choices:
A:Yes
B:No
|
B
|
mathverse_vi_2918
|
|
<image>Do the following graph have inverse functions?
Choices:
A:Yes
B:No
|
A
|
mathverse_vi_2923
|
|
<image>Do the following graph have inverse functions?
Choices:
A:Yes
B:No
|
A
|
mathverse_vi_2928
|
|
<image>Do the following graph have inverse functions?
Choices:
A:Yes
B:No
|
B
|
mathverse_vi_2933
|
|
<image>$f(x)=\ln x$.
Hence state the equation of $g(x)$.
|
$g(x)=\ln x+4$
|
mathverse_vi_2938
|
|
<image>The graph of $f(x)=\ln x$ (gray) and $g(x)$ (black) is drawn below.
What sort of transformation is $g(x)$ of $f(x)$ ?
Choices:
A:Vertical dilation
B:Vertical translation
C:Reflection
D:Horizontal translation
|
A
|
mathverse_vi_2943
|
|
<image>What is the slope of the figure?
Choices:
A:0
B:1
C:6
D:Undefined
|
D
|
mathverse_vi_2948
|
|
<image>What is the slope of the figure?
|
-2
|
mathverse_vi_2953
|
|
<image>What is the slope of the figure?
|
=\frac{7}{4}
|
mathverse_vi_2958
|
|
<image>What is the equation of the figure in blue?
|
$x=0$
|
mathverse_vi_2963
|
|
<image>Mio bought a tablet and pays monthly for internet service for it. She graphed the relationship between the number of months she has had the tablet and the total amount she has spent on it.
What does the y-intercept represent in this context?
Choose 1 answer:
Choices:
A:The number of months after which the total cost is 0 dollars.
B:The cost of buying the tablet
C:The cost per month of internet service
D:None of the above
|
B
|
mathverse_vi_2968
|
|
<image>Find the equation of the figure.
Use exact numbers.
y = _ x + _
|
$y=x-5$
|
mathverse_vi_2973
|
|
<image>Write an equation that represents the figure.
Use exact numbers.
|
$y+3=\frac{3}{4}(x-2)$
|
mathverse_vi_2978
|
|
<image>How many solutions
does the system have?
Choices:
A:One
B:Two
C:Three
D:Four
|
D
|
mathverse_vi_2983
|
|
<image>Whether the curve is the graph of a function.
Choices:
A:Yes
B:No
|
A
|
mathverse_vi_2988
|
|
<image>The graph shows $y_1=x^3$ and $y_2$. Write an equation for $y_2$ as shown in the graph.
|
$y_2=(x+2)^3=y_1(x+2)$
|
mathverse_vi_2993
|
|
<image>A rectangle is inscribed between $y=36-x^2$, as shown in the figure below. Write the area $A$ of the rectangle as a function of $x$.
|
$72 x-2 x^3$
|
mathverse_vi_2998
|
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