Free Printable Performance Final Review Spring 2020

1.

Which of the following functions has a domain restriction?

a)

$f\left(x\right)=3\left(2\right)^x-1$

b)

$f\left(x\right)=4\log_3\left(x-1\right)$

c)

$f\left(x\right)=-x^2+4x-7$

d)

$f\left(x\right)=\left|x-2\right|$

2.

What is the domain of the function $f\left(x\right)=\sqrt{x-3}+2$ ?

a)

$\left[3,\infty\right)$

b)

$\left(-\infty,\infty\right)$

c)

$\left(2,\infty\right]$

d)

$\left[-3,\infty\right)$

3.

Is the function $f\left(x\right)=1,234\left(.85\right)^x$ an example of exponential growth or decay, and what is the percentage of growth or decay?

a)

decay of 15%

b)

growth of 85%

c)

decay of 85%

d)

growth of 23.4%

4.

In the function $f\left(x\right)=1,234\left(1.875\right)^{.12x}$ , what is the initial value?

a)

1,234

b)

1.875

c)

87.5%

d)

.12

5.

Betty has discovered that her cilantro plant has a growth pattern that follows the function $h\left(t\right)=5.1\left(1.075\right)^t$ , where $h$ is the height in cm and $t$ is the time in weeks. What is the rate at which her cilantro plant is growing at?

a)

7.5%

b)

107.5%

c)

5.1%

d)

75%

6.

Betty has discovered that her cilantro plant is growing at a rate that follows the function $h\left(t\right)=5.1\left(1.075\right)^t$ , where $h$ is the height in cm and $t$ is the time in weeks. How tall will the cilantro play be after 20 weeks?

a)

21.7 cm

b)

127,278.5 cm

c)

5.3 cm

d)

5.1 cm

7.

Which function is an example of exponential decay?

a)

$f\left(x\right)=31.7e^{-3x}$

b)

$f\left(x\right)=-\left(1.874\right)^x+4$

c)

$f\left(x\right)=.5e^x-13.75$

d)

$f\left(x\right)=14\left(\frac{7}{6}\right)^x-4$

8.

Is $f\left(x\right)=1.4e^{\left(x+4\right)}-5$ an example of exponential growth or decay, and why?

a)

growth, because the base, $e$ , is greater than 1

b)

decay, because you are subtracting 5

c)

growth, because you are multiplying by 1.4 and that is greater than 1

d)

decay, because there is a horizontal shift to the left 4

9.

Which function below is a horizontal shift to the right of the function $f\left(x\right)=\log_3x$ ?

a)

$g\left(x\right)=2\log_3\left(x-5\right)-4$

b)

$g\left(x\right)=-3\log_3\left(x+3\right)+9$

c)

$g\left(x\right)=\frac{1}{3}\log_3\left(x\right)+4$

d)

$g\left(x\right)=-\log_3\left(x\right)-7$

10.

Which function is a horizontal compression of $\frac{1}{2}$ of the function $f\left(x\right)=\sqrt{x-3}$ ?

a)

$g\left(x\right)=\sqrt{2x-6}$

b)

$g\left(x\right)=\frac{1}{2}\sqrt{x}$

c)

$g\left(x\right)=\sqrt{\frac{1}{2}x}$

d)

$g\left(x\right)=\sqrt{x-3}+\frac{1}{2}$

11.

What is the range of the function $f\left(x\right)=3+\sqrt{x-7}$ ?

a)

$y\ge3$

b)

$x\ge3$

c)

$y\ge7$

d)

$x\ge7$

12.

What is the range of the function $f\left(x\right)=7\log_2\left(x\right)-3$ ?

a)

All Real Numbers

b)

$x\ge7$

c)

$y\ge-3$

d)

$y\ge7$

13.

What is the domain of the function $f\left(x\right)=3\log_2\left(x-4\right)+5$ ?

a)

$x>4$

b)

$x>-4$

c)

$x>3$

d)

$x\ge5$

14.

Which function below is a reflection over the y-axis of the function $f\left(x\right)=\log_3x$ ?

a)

$g\left(x\right)=-2\log_3x$

b)

$g\left(x\right)=\log_3\left(x-3\right)$

c)

$g\left(x\right)=\frac{1}{2}\log_3\left(-x-4\right)$

d)

$g\left(x\right)=\log_3\left(x\right)-4$

15.

What is the domain of the function $f\left(x\right)=-2\log_3\left(x+4\right)+5$ ?

a)

$x\le-4$

b)

$x>-4$

c)

$x<-2$

d)

$y\ge5$

16.

Poppy is always thinking about the future and wants to save money to buy a house in 8 years. She thinks that a $50,000 deposit on a house is a good start. She also found a bank that is going to pay her 9.5% interest compounded monthly. How much should her initial investment be in order to have $50,000 after 8 years?

a)

$23,453.41

b)

$24,191.78

c)

$8.23

d)

$239.17

17.

Marty needs $7,500 to go back to the future. He has 10 years before he needs to go back and he found a bank that will pay him 6.75% yearly interest. How much money should he invest in order to have $7,500 after 10 years?

a)

$3902.86

b)

$43.14

c)

$2,591.36

d)

$14,412.53

18.

List the following in order from least to greatest:
A) $\log_530$
B) $\log_{0.25}32$
C) $\log_749$
D) $\log_840$

a)

B,D,C,A

b)

A,B,C,D

c)

A,B,D,C

d)

B,D,A,C

19.

Rewrite $1.6^{\left(x+2\right)}=14.1$ as a logarithm.

a)

$\log_{1.6}14.1=x+2$

b)

$\log_{14.1}\left(x+2\right)=1.6$

c)

$\log_{1.6}\left(x+2\right)=14.1$

d)

$\log_{\left(x+2\right)}1.6=14.1$

20.

Rewrite $\log_x95=2.3$ in exponential form.

a)

$x^{2.3}=95$

b)

$2.3^{95}=x$

c)

$95^{2.3}=x$

d)

$x^{95}=2.3$

21.

Solve for x. Check for extraneous solutions.
$\log_2\left(x\right)+4=2$

a)

$\frac{1}{4}$

b)

$512$

c)

$81$

d)

$\frac{1}{5}$

22.

Solve for x. Check for extraeous solutions.
$\log\left(x\right)+\log\left(x+3\right)=1$

a)

2

b)

5

c)

-2

d)

-5

23.

Solve for x. Check for extraneous solutions.

$\log_5\left(4x-7\right)=\log_5\left(x+5\right)$

a)

$4$

b)

$3$

c)

$12$

d)

$7$

24.

Solve for x. Check for extraneous solutions.

$\log_7x-\log_73=2$

a)

$147$

b)

$21$

c)

$49$

d)

$\frac{49}{3}$

25.

Solve for x. Round your answer to the nearest hundredth.

$e^{\left(x+2\right)}=300$

a)

$7.70$

b)

$3.70$

c)

$5.70$

d)

$298$

26.

Solve for x, be sure to check for extraneous solutions. $-8+\sqrt{5x-5}=-3$

a)

$6$

b)

$4$

c)

$3$

d)

no solution

27.

Solve for x.

$3_{\sqrt{7x+5}}=-3$

a)

$\frac{-32}{7}$

b)

$2$

c)

$\frac{-27}{7}$

d)

$\frac{27}{7}$

28.

Which function below has a maximum of 2?

a)

$f\left(x\right)=-x^2+8x-14$

b)

$f\left(x\right)=\sqrt{x-4}+2$

c)

$f\left(x\right)=\left|x+2\right|$

d)

$f\left(x\right)=4\log_32x$

29.

Which function has a minimum of -3?

a)

$f\left(x\right)=2\sqrt{x+5}-3$

b)

$f\left(x\right)=-\log_2\left(x-3\right)+4$

c)

$f\left(x\right)=\left|x-3\right|+3$

d)

$f\left(x\right)=x^3-3$

30.

Which function approaches $-\infty$ as $x\rightarrow\infty$ ?

a)

$f\left(x\right)=-2e^x-6$

b)

$f\left(x\right)=3x^2-8x$

c)

$f\left(x\right)=\log_2\left(-x\right)$

d)

$f\left(x\right)=\sqrt{-2x+5}-7$

31.

What is Ms. Smith's average rate of change from 0-2 seconds?

a)

2.5 feet per second

b)

4 feet per second

c)

$\frac{8}{3}$ feet per second

d)

$\frac{2}{5}$ feet per second

32.

What is Ms. Smith's average rate of change from 6-15 seconds?

a)

$\frac{-10}{9}$ feet per second

b)

-10 feet per second

c)

$\frac{-4}{3}$ feet per second

d)

$\frac{2}{3}$ feet per second

Performance Final Review Spring 2020

Total questions: 32

Worksheet time: 3hrs 40mins

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