id stringclasses 2
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values | image imagewidth (px) 383 1.11k | subquestions listlengths 5 5 | final_question stringclasses 2
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15 | What is the value of f(0)? | [
{
"answer": "g(x) = 0.5^x",
"question": "What is the function represented in the graph?"
},
{
"answer": "x = 0",
"question": "What is the input value of x for which we need to find the function's value?"
},
{
"answer": "1",
"question": "What is 0.5 raised to the power of 0?"
},
{... | What is the sum of the function's values at the y-intercept and at x = -3? | The function displayed in the graph is g(x) = 0.5^x.
1. The value at the y-intercept (where x=0) is g(0) = 0.5^0 = 1. This can be verified on the graph, as the curve crosses the y-axis at y=1.
2. The value at x = -3 is g(-3) = 0.5^-3 = (1/2)^-3 = 2^3 = 8. This can be verified on the graph by finding x=-3 on the horiz... | |
4 | What is f(0.5)? | [
{
"answer": "m/N",
"question": "What is represented on the x-axis of the graph?"
},
{
"answer": "1/N",
"question": "What is represented on the y-axis of the graph?"
},
{
"answer": "m/N = 0.5",
"question": "According to the x-axis, what value should be used for calculation?"
},
{
... | What is the sum of the y-axis values for all data points located strictly above the horizontal red dashed line? | 1. The horizontal red dashed line is located at a y-axis value of 0.2.
2. Identify all data points with a y-coordinate strictly greater than 0.2. These are:
* One point at y = 0.5 (corresponding to x = 0.5 or m/N = 1/2).
* Two points at y ≈ 0.333 (corresponding to x = 1/3 and x = 2/3; y-value is 1/3).
... |
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