Question

Helppp :((((( pleaseee

Answer 1

Problem 6

Answers: Choice A, Choice C, Choice F

Explanation: For each of these answer choices, y goes up as x does as well. Both increase together. As you move from left to right, the graph goes uphill for these intervals. For something like choice B, notice how y drops from y = 50 to y = 40 as x increases, so there's no way to have a positive rate of change. The term "rate of change" is effectively the slope of the straight line through the two points.

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Problem 7

I'll do the first two to get you started

For part A, we're looking at the points (-3,0) and (-2,2). Note the x coordinates x = -3 and x = -2

Find the slope of the line through these two points

m = (y2-y1)/(x2-x1)

m = (2-0)/(-2-(-3))

m = 2

Answer to part A is 2

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Same idea, but now we'll use the two points (-2,2) and (1,-4)

m = (y2-y1)/(x2-x1)

m = (-4-2)/(1-(-2))

m = -2

Answer to part B is -2

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Problem 8

Answer: The function is positive on two intervals $-3 < x < -1$ and $x > 2$

Explanation:

We're looking where the curve is above the x axis. The first portion above the x axis is from x = -3 to x = -1, excluding those endpoints (since the endpoints are on the x axis itself). The other portion above the x axis is everything to the right of x = 2

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Problem 9

Answer: The function is negative on two intervals $x < -3$ and $-1 < x < 2$

Explanation:

Similar to problem 8, but we're now looking below the x axis. The first portion below the x axis is from negative infinity up to x = -3, excluding the endpoints. The other portion is between -1 and 2, excluding those endpoints as well.

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Problem 10

Answers: -3, -1, and 2

Explanation:

The zeros are also known as the roots or x intercepts. I prefer the term "root" or "x intercept" because the term "zero" might imply that the root has to always be x = 0, but that isn't the case. The x intercept can be anything you want. The graph shows three x intercepts where the curve crosses or touches the x axis. These locations are -3, -1 and 2 on the x axis.

We can say the x intercepts are (-3,0), (-1,0) and (2,0), but that's a bit cumbersome. It's easier to say "roots are -3, -1, and 2".