Quiz about College Algebra Test 3 Review - Autumn 2024

Question 1

List all possible rational zeros of the function $$f\left(x\right)\ =\ 2x^{5\ }-\ 12x^{2\ }-8x+10$$

Accepted Answer

$$\left\{\pm1,\ \pm2,\ \ \pm5,\ \pm\ 10,\ \pm\frac{1}{2},\ \pm\frac{5}{2}\right\}$$

Answer

$$\left\{\pm1,\ \pm2,\ \pm5,\ \pm10,\ \pm\frac{1}{5},\ \pm\frac{2}{5}\right\}$$

Answer

$$\left\{\pm1,\ \pm2,\ \pm5,\ \pm10\right\}$$

Question 2

Convert $$\log_3\ x\ =\ 7$$ to exponential form.

Accepted Answer

$$3^7\ =\ x$$

Answer

$$3^x\ =\ 7$$

Question 3

Convert $$x^{9\ }=\ 7$$ to logarithmic form.

Accepted Answer

$$\log_x\ 7\ =\ 9$$

Answer

$$\log_x\ 9\ =\ 7$$

Question 4

For the function below, find the vertical asymptotes and the horizontal asymptotes.

$$f\left(x\right)\ =\ \frac{x^{2\ }-\ 3x\ +\ 2\ }{2x\ -\ 10}$$

Accepted Answer

VA: x = 5

HA: None

Answer

VA: x = 5

HA: y = 0

Answer

VA: x = 5

HA: y = 1/2

Answer

VA: None

(Hole at x = 5)

HA: None

Question 5

For the function below, find the vertical asymptotes and the horizontal asymptotes.

$$g\left(x\right)\ =\ \frac{-4x\ +\ 10}{9x\ +\ 2}$$

Accepted Answer

VA: x = -2/9

HA: y = -4/9

Answer

VA: x = 2/9

HA: y = -4/9

Answer

VA: x = 5/2

HA: y = -4/9

Answer

VA: x = -4/9

HA: None

Question 6

Find the value of $$f\left(2\right)$$ for the function $$f\left(x\right)\ =\ x^{4\ }-\ 3x^{3\ }+\ 11x\ -\ 10$$ .

Accepted Answer

4

Answer

10

Answer

8

Answer

-52

Question 7

Find the inverse of the function $$f\left(x\right)\ =\ 12x\ -\ 3$$ .

Accepted Answer

$$f^{-1}\left(x\right)\ =\ \frac{x}{12}\ +\ \frac{1}{4}$$

Answer

$$f^{-1}\left(x\right)\ =\ 3x\ -\ 12$$

Answer

$$f^{-1}\left(x\right)\ =\ \frac{x}{12}\ -\ \frac{1}{4}$$

Answer

$$f^{-1}\left(x\right)\ =\ -\frac{x}{12}\ +\ 3$$

Question 8

Solve the inequality $$\frac{8-x}{x+7}\le\ 0$$

Accepted Answer

$$\left(-\infty,\ -7\right)\ \cup\ \left[8,\ \infty\right)$$

Answer

$$\left(-\infty,\ -7\right]\ \cup\ \left[8,\ \infty\right)$$

Answer

$$\left[-7,\ 8\right]$$

Answer

$$\left(-7,\ 8\right]$$

Question 9

Evaluate $$\log_28\ +\ \log_636\ -\ \log_327$$

Accepted Answer

2

Answer

0

Answer

1

Answer

3

Question 10

Which expression below is equivalent to $$\ln\left(\frac{x^2\sqrt{y}}{z^3}\right)$$ ?

Accepted Answer

$$2\ln x\ +\ \frac{1}{2}\ln y\ -\ 3\ln z$$

Answer

$$2\ln x\ +\ \ln y\ -\ 3\ln z$$

Answer

$$2\ln x\ -\ \frac{1}{2}\ln y\ +\ 3\ln z$$

Answer

$$2\ln x\ +\ \frac{1}{2\ln y}\ -\ \frac{1}{3\ln z}$$

Question 11

Solve the system given:
3x - y = 7
2x + y = 3

Accepted Answer

(2,-1)

Answer

(-1,2)

Answer

(5,4)

Answer

(4,5)

Question 12

Solve the following system.

Accepted Answer

(-8, -6) and (6,8)

Answer

(10,8) and (-8, -10)

Answer

no solution

Answer

(6, 8) and (8, 10)

Question 13

Find the domain of the function $$f\left(x\right)\ =\ \log_4\left(x-8\right)\ +\ 6$$ .

Accepted Answer

$$\left(8,\ \infty\right)$$

Answer

$$\left(-8,\ \infty\right)$$

Answer

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

Answer

$$\left(6,\ \infty\right)$$

Question 14

Find the range of the function $$f\left(x\right)\ =\ \log_4\left(x-8\right)\ +\ 6$$ .

Accepted Answer

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

Answer

$$\left(8,\ \infty\right)$$

Answer

$$\left(-8,\ \infty\right)$$

Answer

$$\left(6,\ \infty\right)$$

Question 15

State the domain of the function $$f\left(x\right)\ =\ -4^{\left(x+3\right)}\ -\ 13$$ .

Accepted Answer

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

Answer

$$\left(-13,\ \infty\right)\ $$

Answer

$$\left(\infty,\ -13\right)$$

Answer

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

Question 16

State the range of the function $$f\left(x\right)\ =\ -4^{\left(x+3\right)}\ -\ 13$$ .

Accepted Answer

$$\left(\infty,\ -13\right)$$

Answer

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

Answer

$$\left(-13,\ \infty\right)\ $$

Answer

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

Question 17

Find the inverse of the function $$y\ =\ x^2\ +6x\ +\ 9$$ .

Accepted Answer

$$y^{-1}\ =\ \sqrt{\ x}\ -\ 3$$

Answer

$$y^{-1}\ =\ \sqrt{\ x}\ +3$$

Answer

$$y^{-1}\ =\ \ \sqrt{\ x+3}$$

Answer

$$y^{-1}\ =\ \sqrt{\ x-3}$$

Question 18

Find the inverse of the function $$y\ =\ \sqrt{x-7\ }$$ .

Accepted Answer

$$y^{-1\ }=\ x^{2\ }+\ 7$$

Answer

$$y^{-1}\ =\ x^{2\ }-7$$

Answer

$$y^{-1\ }=\ \left(x+7\right)^2$$

Answer

$$y^{-1}\ =\ \left(x-7\right)^2$$

Question 19

Simplify the logarithm $$\log_63\ +\ \log_612$$ .

Accepted Answer

2

Answer

4

Answer

36

Answer

15

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