Question

what is the range of the function shown on the graph above?
a. $-2 \leq y \leq -7$

b. $-7 \leq y \leq -2$

c. $-8 \leq y \leq 8$

d. $-9 \leq y \leq 8$

Explanation:

Step1: Identify the highest and lowest y - values

The range of a function is the set of all possible y - values (outputs) of the function. From the graph, we need to find the maximum (highest) y - value and the minimum (lowest) y - value of the function's graph.

Looking at the graph, the highest point (maximum y - value) appears to be at \(y = 8\) (by observing the grid and the position of the top point of the line segment) and the lowest point (minimum y - value) appears to be at \(y=- 9\) (by observing the grid and the position of the bottom point of the line segment). Wait, no, let's re - examine. Wait, the options: Let's check the y - coordinates of the two endpoints of the line segment. The top endpoint: Let's assume each grid square is 1 unit. If we look at the y - axis, the top point is at \(y = 8\) (since from the origin, moving up 8 units) and the bottom point is at \(y=-9\) (moving down 9 units from the origin). Wait, but let's check the options. Option D is \(-9\leq y\leq8\). Let's verify the other options. Option A and B have very small ranges, which don't match the graph. Option C has a range from - 8 to 8, but the bottom point is lower than - 8 (at - 9) and the top is at 8. So the range should be from the minimum y - value to the maximum y - value of the graph. The minimum y - value here is - 9 and the maximum is 8, so the range is \(-9\leq y\leq8\).

Step2: Match with the options

Now we compare with the given options:

• Option A: \(-2\leq y\leq - 7\) is incorrect as the range is much larger.
• Option B: \(-7\leq y\leq - 2\) is incorrect for the same reason.
• Option C: \(-8\leq y\leq8\) is incorrect because the minimum y - value is - 9, not - 8.
• Option D: \(-9\leq y\leq8\) matches the minimum and maximum y - values we identified from the graph.

Answer:

D. \(-9\leq y\leq8\)