Quiz about Midterm Review

Question 1

Which of the following represents the given number in set builder notation?

{. . . -7, -6, -5, -4}

Accepted Answer

$$\left\{x\ :\ x\le-4,\ x\in Z\right\}$$

Answer

$$\left\{x\ :\ x\ge-7,\ x\in Z\right\}$$

Answer

$$\left\{x\ :\ x\ge-4,\ x\in Z\right\}$$

Answer

$$\left\{x\ :\ x\le-7,\ x\in Z\right\}$$

Question 2

Which of the following represents the set of all multiples of 7?

Accepted Answer

$$\left\{x\ :\ x=7n,\ x\in Z\right\}$$

Answer

$$\left\{x\ :\ x\ \le7,\ x\ \in Z\right\}$$

Answer

$$\left\{x\ :\ x\ge7n,\ x\ \in Z\right\}$$

Answer

$$\left\{x\ :\ x<7n,\ x\in Z\right\}$$

Question 3

State the domain of the function $$g\left(x\right)=\sqrt[]{x^2-4}$$ .

Accepted Answer

$$\left\{x\ :\ x\ \ge\pm2,\ x\in R\right\}$$

Answer

$$\left\{x\ :\ x e\pm4,\ x\in R ight\}$$

Answer

$$\left\{x\ :\ x\ >\pm2,\ x\in R\right\}$$

Answer

$$\left\{x\ :\ x\ <\pm2,\ x\ \in R\right\}$$

Question 4

Find the domain of the function $$h\left(x\right)=\frac{2x-7}{x^2+4x+4}$$

Accepted Answer

$$\left\{x\ :\ x\ >-2,\ x\in R\right\}$$

Answer

$$\left\{x\ :\ x\ \ge2,\ x\in R\right\}$$

Answer

$$\left\{x\ :\ x e-2,\ x\in R ight\}$$

Answer

$$\left\{x\ :\ x\ <-2,\ x\in R\right\}$$

Question 5

Find each function value if $$f\left(x\right)=3x^2+7$$ , find $$f\left(5\right).$$

Accepted Answer

82

Answer

80

Answer

81

Answer

83

Question 6

If $$g\left(x\right)=\left\{x\ +12\ if\ x\le-1\ and\ 67-x\ if\ x>-1\right\}$$

Find $$g\left(-2\right)\ and\ g\left(54\right).$$

Accepted Answer

10;13

Answer

10; 12

Answer

10;15

Answer

10;17

Question 7

Find the domain and range of the given graph.

Accepted Answer

$$D:\left\{x\ :\ x\ >-5,\ x\in R\right\}$$ $$R:\left\{y\ :\ y\ge-3,\ y\in R\right\}$$

Answer

$$D:\left\{x:x>-5,\ x\in R\right\}$$ $$R:\left\{y:y\ge3,\ y\in R\right\}$$

Answer

$$D:\left\{x\ :\ x>-5,\ x\in R\right\}$$ $$R:\left\{y\ :\ y\ >-3,\ y\in R\right\}$$

Answer

$$D:\left\{x\ :\ x\ >-5,\ x\in R\right\}$$ $$R:\ \left\{y\ :\ y<-3,\ y\in R\right\}$$

Question 8

Fine the inverse of the function and restriction of the domain

$$f\left(x\right)=3x-6.$$

Accepted Answer

$$f^{-1}\left(x\right)=\frac{x+6}{3}.$$ $$D:\left\{x\ :\ x\in R\right\}$$

Answer

$$f^{-1}\left(x\right)=x+3$$

$$D:\left\{x\ :\ x\in R\right\}$$

Answer

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

$$D:\ \left\{x\ :\ x\in R\right\}$$

Answer

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

$$D:\left\{x\ :\ x\in R\right\}$$

Question 9

Solve the given equation $$\sqrt[]{\sqrt[3]{2x\ +\ 3}}=\ 2.$$

Accepted Answer

30.5

Answer

29.5

Answer

31.5

Answer

32.5

Question 10

Solve the given equation $$\sqrt[3]{x\ +\ 9+\sqrt[]{3x}}=3.$$

Accepted Answer

12

Answer

10

Answer

11

Answer

13

Question 11

Determine the equation of the function after the given transformation.

$$f\left(x\right)=5^x$$ translate 3 units right and 4 units up.

Accepted Answer

$$f\left(x\right)=5^{\left(x-3\right)}+4$$

Answer

$$f\left(x\right)=5^{\left(x+4\right)}+3$$

Answer

$$f\left(x\right)=5^{\left(x+3\right)}-4$$

Answer

$$f\left(x\right)=5^{\left(x-4\right)}-3$$

Question 12

Solve the given equation.

$$x\ +\frac{6}{x}=-5.$$

Accepted Answer

-2, -3

Answer

-1, -3

Answer

-3, 4

Answer

5, -6

Question 13

Find the value of x in the equation

$$\frac{3}{x\ +1}+\frac{7}{2-x}=\frac{-4}{x-1}.$$

Accepted Answer

$$\frac{5}{13}$$

Answer

$$\frac{2}{13}$$

Answer

$$\frac{7}{13}$$

Answer

$$\frac{9}{13}$$

Question 14

Use Maclaurin polynomials to approximate the powers of e to the hundredths place.

$$e^5$$

Accepted Answer

148.41

Answer

149.21

Answer

151.34

Answer

176.92

Question 15

What is the logarithmic form of

$$3^{-3}=\frac{1}{27}$$

Accepted Answer

$$\log_3\frac{1}{27}=-3$$

Answer

$$\log_{-3}3=27$$

Answer

$$\log_{-3}\frac{1}{27}=3$$

Question 16

Find the value of $$\log_222.5$$ Using the change of base.

Accepted Answer

4.49

Answer

3.24

Answer

2.76

Answer

1.34

Question 17

Evaluate $$\log_{\sqrt[]{4}}64.$$

Accepted Answer

6

Answer

3

Answer

4

Answer

5

Question 18

Condense

$$\frac{1}{3}\log_{ }\left(x+2\right)-\log_{ }\left(x+3\right).$$

Accepted Answer

$$\log_{ }\frac{\sqrt[3]{x+2}}{x+3}$$

Answer

$$\log_{ }\left(\frac{x+2}{x+3}\right)$$

Answer

$$\log_{ }\left(x+2\right)\left(x+3\right)$$

Answer

$$\log_{ }\left(\sqrt[3]{x+2}\right)\left(x+3\right)$$

Question 19

$$e^{\ln x^2}$$

Accepted Answer

$$x^2$$

Answer

$$\ln e$$

Answer

$$e^2$$

Answer

$$x$$

Midterm Review

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