Question

transition 1 the results of a poll that asks americans whether they used the internet yesterday can be modeled as a function. sketch a graph that shows the number of people polled that responded yes to the survey, y, as a function of time x, months since january 2005. positive: for time greater than 0 months... increasing: for all time greater than 0 months... intercepts: the graph intersects the y - axis at about (0, 55)... end behavior: as x increases, y increases. the total number of people polled is the maximum x could ever reach in the maximum number of people surveyed. then there are four graphs (a, b, c, d) with titles did you use the internet yesterday? and axes months since january 2005 (x - axis) and yes responses (y - axis). each graph has a curve. options a, b, c, d with radio buttons.

Explanation:

To solve this, we analyze the key requirements: the graph should have a \( y \)-intercept (at \( x = 0 \), months since January 2005) around 55 - 58 (as per the "Intrepreting" note: "The graph should cross the \( y \)-axis at about 55 - 58"). Also, the function is increasing (since the number of people using the internet should grow over time) and concave (the rate of increase might slow, typical of growth curves).

Step 1: Analyze the \( y \)-intercept

• Option A: At \( x = 0 \), the \( y \)-value (no responses) is around 55 - 60, matching the required range.
• Option B: The \( y \)-intercept is too low (below 55).
• Option C: The \( y \)-intercept is near 0, which is incorrect (we expect a non - zero initial value).
• Option D: The \( y \)-intercept is misaligned (the starting point does not match 55 - 58).

Step 2: Analyze the shape (increasing, concave)

• Option A shows an increasing, concave curve (curving upwards, but the rate of increase slows, which is consistent with a growth function where saturation might occur). The other options either have incorrect intercepts or shapes.

Answer:

A. Did You Use the Internet Yesterday? (with the corresponding graph)