Quiz about AP Precalculus Unit 1A Review

Question 1

On what interval is the average rate of change positive?

Accepted Answer

(-1, 1) U ( 3, 4)

Answer

(-1,1) & (3,4)

Answer

(-3,-2)

Answer

(-3, 0) U (2, 4)

Question 2

On what interval is the average rate of change increasing?

Accepted Answer

(-3, 0) u (2, 4)

Answer

(-3, -1) u (1, 3)

Answer

(-1, 1) u (3, 4)

Answer

(0, 2)

Question 3

On what interval is the average rate of change decreasing?

Accepted Answer

(0, 2)

Answer

(-3, -1) u (1, 3)

Answer

(-1, 1) u (3, 4)

Answer

(-3, 0) u (2, 4)

Question 4

Find the point(s) of inflection (if it exists) of the graphed function.

Accepted Answer

Points 3 and 5

Answer

No point of inflection

Answer

Points 1, 3, 5 and 7

Answer

Points 1, 2, 3, 4, 5, 6 and 7

Answer

Points 2, 4 and 6

Question 5

Identify any relative maximums of the graphed function.

Accepted Answer

Point 4

Answer

No relative maximums

Answer

Points 2 and 6

Answer

Points 1, 4, and 7

Answer

Points 1, 3, 4, 5, and 7

Question 6

Identify any relative minimums of the graphed function.

Accepted Answer

Points 2 and 6

Answer

No relative minimums

Answer

Point 4

Answer

Points 1, 4, and 7

Answer

Points 1, 2, 3, 5, 6, and 7

Question 7

What kind of interval represents where the function is positive and decreasing?

Accepted Answer

Anywhere the graph is above the x-axis and the y-values are getting smaller.

Answer

Anywhere the graph is concave up with a negative slope.

Answer

Anywhere the graph is concave down with a positive slope.

Answer

Anywhere the graph is below the x-axis and the y-values are getting bigger.

Question 8

What kind of interval represents where the function is negative and increasing?

Accepted Answer

Anywhere the graph is below the x-axis and the y-values are getting bigger.

Answer

Anywhere the graph is above the x-axis and the y-values are getting smaller.

Answer

Anywhere the graph is concave up with a negative slope.

Answer

Anywhere the graph is concave down with a positive slope.

Question 9

What kind of interval represents where the rate of change is negative and increasing?

Accepted Answer

Anywhere the graph is concave up with a negative slope.

Answer

Anywhere the graph is above the x-axis and the y-values are getting smaller.

Answer

Anywhere the graph is concave down with a positive slope.

Answer

Anywhere the graph is below the x-axis and the y-values are getting bigger.

Question 10

What kind of interval represents where the rate of change is positive and decreasing?

Accepted Answer

Anywhere the graph is concave down with a positive slope.

Answer

Anywhere the graph is above the x-axis and the y-values are getting smaller.

Answer

Anywhere the graph is concave up with a negative slope.

Answer

Anywhere the graph is below the x-axis and the y-values are getting bigger.

Question 11

What kind of interval represents where the rate of change is positive and increasing?

Accepted Answer

Anywhere the graph is concave up with a positive slope.

Answer

Anywhere the graph is above the x-axis and the y-values are getting bigger.

Answer

Anywhere the graph is concave up and above the x-axis.

Answer

Anywhere the graph is above the x-axis with a positive slope.

Question 12

What kind of interval represents where the rate of change is negative and decreasing?

Accepted Answer

Anywhere the graph is concave down with a negative slope.

Answer

Anywhere the graph is below the x-axis and the y-values are getting smaller.

Answer

Anywhere the graph is concave down and below the x-axis.

Answer

Anywhere the graph is below the x-axis with a negative slope.

Question 13

What kind of interval represents where the function is positive and increasing?

Accepted Answer

Anywhere the graph is above the x-axis and the y-values are getting bigger.

Answer

Anywhere the graph is concave up with a positive slope.

Answer

Anywhere the graph is concave up and the y-values are getting bigger.

Answer

Anywhere the graph is above the x-axis and concave up.

Question 14

What kind of interval represents where the function is negative and decreasing?

Accepted Answer

Anywhere the graph is below the x-axis and the y-values are getting smaller.

Answer

Anywhere the graph is concave down with a negative slope.

Answer

Anywhere the graph is concave down and the y-values are getting smaller.

Answer

Anywhere the graph is below the x-axis and concave down.

Question 15

The function f is given by $$f\left(x\right)=-2x^7+5x^4+6x^2-3$$ . Which of the following correctly describes the end behavior of f as the input values increase without bound?

Accepted Answer

$$\lim_{x\rightarrow\infty}f\left(x\right)=-\infty$$

Answer

$$\lim_{x\rightarrow\infty}f\left(x\right)=\infty$$

Answer

$$\lim_{x\rightarrow-\infty}f\left(x\right)=\infty$$

Answer

$$\lim_{x\rightarrow-\infty}f\left(x\right)=-\infty$$

Question 16

The function f is given by $$f\left(x\right)=-2x^7+5x^4+6x^2-3$$ . Which of the following correctly describes the end behavior of f as the input values decrease without bound?

Accepted Answer

$$\lim_{x\rightarrow-\infty}f\left(x\right)=\infty$$

Answer

$$\lim_{x\rightarrow\infty}f\left(x\right)=\infty$$

Answer

$$\lim_{x\rightarrow\infty}f\left(x\right)=-\infty$$

Answer

$$\lim_{x\rightarrow-\infty}f\left(x\right)=-\infty$$

Question 17

The graph of a polynomial function $$y=p\left(x\right)$$ is shown. Which of the following expressions could define $$p\left(x\right)$$ ?

Accepted Answer

$$\left(x+3\right)^2\left(x-2\right)^2$$

Answer

$$\left(x-2\right)\left(x+3\right)$$

Answer

$$\left(x+3\right)\left(x-2\right)$$

Answer

$$\left(x-3\right)^2\left(x+2\right)^2$$

Question 18

Calculate the average rate of change from 20 to 40 minutes.

Accepted Answer

-2 gallons per minute

Answer

-2 minutes per gallon

Answer

-20 minutes per gallon

Answer

-20 gallons per minute

Question 19

The graph of the function $$f$$ is given for $$-3\le x\le6$$ Which of the following statements about the rate of change of $$f$$ over the interval $$-2

Accepted Answer

The rate of change is increasing.

Answer

The rate of change is positive.

Answer

The rate of change is negative.

Answer

The rate of change is decreasing.

Question 20

The figure shows a swimming pool filled with water. A pump is used to remove water from the pool until the pool is empty. When the pump is running, the rate at which the volume of water in the pool decreases is constant. During the first two hours, the pump works slower than usual due to a broken piece. Then the pump stops working. The broken piece is replaced, and the pump works at its usual rate until the pool is completely emptied of water. The entire process of emptying the pool takes six hours. Which of the following graphs could depict this situation, where time, in hours, is the independent variable, and the volume of water in the pool, in gallons, is the dependent variable?

Accepted Answer

Question 21

The figure shows the graph of a function $$f$$ . The zero and extrema for $$f$$ are labeled, and the point of inflection of the graph of $$f$$ is labeled. Let $$A$$ , $$B$$ , $$C$$ , $$D$$ , and $$E$$ represent the $$x$$ -coordinates at those points. Of the following, on which interval is $$f$$ decreasing and the graph of $$f$$ concave up?

Accepted Answer

from $$C$$ to $$D$$

Answer

from $$A$$ to $$B$$

Answer

from $$B$$ to $$C$$

Answer

from $$D$$ to $$E$$

Question 22

The function $$f$$ is given by $$f\left(x\right)=-3x^8+7x^5-3x^4+2x-4$$ . Which of the following correctly describes the end behavior of $$f$$ as the input values decrease without bound?

Accepted Answer

$$\lim_{x\rightarrow-\infty}f\left(x\right)=-\infty$$

Answer

$$\lim_{x\rightarrow\infty}f\left(x\right)=\infty$$

Answer

$$\lim_{x\rightarrow-\infty}f\left(x\right)=\infty$$

Answer

$$\lim_{x\rightarrow\infty}f\left(x\right)=-\infty$$

Question 23

The function $$f$$ is given by $$f\left(x\right)=-3x^8+7x^5-3x^4+2x-4$$ . Which of the following correctly describes the end behavior of $$f$$ as the input values increase without bound?

Accepted Answer

$$\lim_{x\rightarrow\infty}f\left(x\right)=-\infty$$

Answer

$$\lim_{x\rightarrow\infty}f\left(x\right)=\infty$$

Answer

$$\lim_{x\rightarrow-\infty}f\left(x\right)=\infty$$

Answer

$$\lim_{x\rightarrow-\infty}f\left(x\right)=-\infty$$

Question 24

The figure shown is the graph of a polynomial function $$g$$ .

Which of the following could be an expression for $$g\left(x\right)$$ ?

Accepted Answer

$$0.25\left(x-5\right)^2\left(x-1\right)\left(x+8\right)$$

Answer

$$0.25\left(x-5\right)\left(x-1\right)\left(x+8\right)$$

Answer

$$0.25\left(x+5\right)\left(x+1\right)\left(x-8\right)$$

Answer

$$0.25\left(x+5\right)^2\left(x+1\right)\left(x-8\right)$$

Question 25

A polynomial function $$p$$ is given by $$p\left(x\right)=-x\left(x-4\right)\left(x+2\right)$$ .

What are all intervals on which $$p\left(x\right)\le0$$ ?

Accepted Answer

$$\left[-2,0\right]\cup\left[4,\infty\right)$$

Answer

$$\left[-2,4\right]$$

Answer

$$\left(-\infty,-4\right]\cup\left[0,2\right]$$

Answer

$$\left(-\infty,-2\right]\cup\left[0,4\right]$$

Question 26

Is the interval represented in the table concave up, concave down, or neither?

Accepted Answer

Concave Up

Answer

Concave Down

Answer

Neither

Question 27

Is the function even, odd, or neither?

$$g\left(x\right)=x^2-2x\ +\ 3$$

Accepted Answer

Neither

Answer

Even

Answer

Odd

Question 28

Is the function even, odd, or neither?

$$h\left(x\right)=-2x^5-x^3+4x$$

Accepted Answer

Odd

Answer

Even

Answer

Neither

Question 29

Is the function even, odd, or neither?

$$p\left(x\right)=x^4-8x^2+5$$

Accepted Answer

Even

Answer

Odd

Answer

Neither

Question 30

Which of the following graphs has the largest average rate of change from -1 to 2?

Accepted Answer

Option A is correct

Answer

B.

Answer

C.

Answer

D.

Question 31

Find the average rate of change of f(x)=2x²+3x-1 from 1 to 2.

Accepted Answer

9

Answer

18

Answer

-9

Answer

3

AP Precalculus Unit 1A Review

48 questions

Check ALL the intervals where this graph is decreasing.

On what intervals is f(x) increasing?

What interval is f(x) < 0 ?

What interval is f(x) < 0 ?

What interval is f(x) > 0 ?

Where is the average rate of change negative?

On what interval is the average rate of change positive?

On what interval is the average rate of change increasing?

On what interval is the average rate of change decreasing?

On what interval is the f(x) positive and increasing?

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