Quiz about Precalculus Midterm

Question 1

Find the inverse of $$g\left(x\right)=\sqrt[]{x-3}$$

Accepted Answer

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

Answer

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

Answer

$$g^{-1}\left(x\right)=\left(x-3\right)^{2\ }$$

Answer

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

Question 2

Solve $$\sqrt[]{x-3}=x-5$$

Accepted Answer

7

Answer

9

Answer

11

Answer

5

Question 3

Let $$p\left(x\right)=3x^3+9x^2-3x-9$$ and state the maximum number of real zeros and the maximum number of relative extrema.

Accepted Answer

Maximum number of real zeros: 3; Maximum number of relative extrema: 2.

Answer

Maximum number of real zeros: 2; Maximum number of relative extrema: 3.

Answer

Maximum number of real zeros: 1; Maximum number of relative extrema: 1.

Answer

Maximum number of real zeros: 4; Maximum number of relative extrema: 0.

Question 4

Find the zeros of $$p\left(x\right)=3x^3+9x^2-3x-9$$

Accepted Answer

x = 1, x = -1, x = -3

Answer

x = 1, x = 1, x = -3

Answer

x = 1, x = -1, x = 3

Answer

x = -1, x = -1, x = -3

Question 5

Divide $$2x^5+3x^4-15x-2$$ by $$x+1$$

Accepted Answer

$$2x^4+x^3-x^2+x-16\ R.14$$

Answer

$$2x^4+x^3+x^2+x-16\ R.14$$

Answer

$$2x^4+x^3-x^2+x+16\ R.14$$

Answer

$$2x^4-x^3-x^2+x-16\ R.14$$

Question 6

Use the Remainder Theorem to find the remainder when $$p\left(x\right)=x^5+3x^2-10$$

is divided by $$x+2$$

Accepted Answer

-30

Answer

34

Answer

50

Answer

10

Question 7

Find all the zeros of $$p\left(x\right)=x^3+x-10$$

Accepted Answer

$$x=2,\ -1\pm2i$$

Answer

$$x=2,\ 1\pm2i$$

Answer

$$x=-2,\ -1\pm2i$$

Answer

$$x=-2,\ 1\pm2i$$

Question 8

Identify any asymptotes and

point discontinuities of $$g\left(x\right)=\frac{1}{x-2}+1$$

Accepted Answer

Vertical asymptote at x = 2; horizontal asymptote at y = 1; no point discontinuities.

Answer

Vertical asymptote at x = 1; horizontal asymptote at y = 0; point discontinuity at x = 2.

Answer

No vertical asymptote; horizontal asymptote at y = 1; point discontinuity at x = 2.

Answer

Vertical asymptote at x = 3; horizontal asymptote at y = 2; no point discontinuities.

Question 9

Solve $$4x-3=\frac{x+13}{x+1}$$

Accepted Answer

x = 2 or x = -2

Answer

x = 0

Answer

x = 3 or x = -3

Answer

x = -1 or x = 1

Question 10

Which of the following relations are functions? List all correct answers.

Accepted Answer

A

Accepted Answer

B

Accepted Answer

D

Answer

C

Question 11

If $$f\left(x\right)=\sqrt[]{x-6}$$ and $$g\left(x\right)=x^2+7$$ write a function rule for $$\left(f\circ g\right)\left(x\right)$$

Accepted Answer

$$f\left(g\left(x\right)\right)=\sqrt[]{x^2+1}$$

Answer

$$f\left(g\left(x\right)\right)=\sqrt[]{x^2-1}$$

Answer

$$f\left(g\left(x\right)\right)=\sqrt[]{x^2}+1$$

Answer

$$f\left(g\left(x\right)\right)=\sqrt[]{x^2}-1$$

Question 12

Are $$f\left(x\right)=x^2+1$$ and $$g\left(x\right)=\sqrt[]{x^2-1}$$ inverse functions?

Accepted Answer

No

Answer

Yes

Question 13

Solve and check for extraneous solutions

Accepted Answer

x=5

Answer

x= -5

Answer

No Solution

Question 14

Solve by cross-multiplying.

Accepted Answer

x = -4, 5

Answer

x = -1, 5

Answer

No Solution

Answer

x= -4

Question 15

Solve for x

Accepted Answer

-4

Answer

4

Answer

2

Answer

-2

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