Question 1

Solve the quadratic equation $$x^2 - 5x + 7x - 35 = 0$. What are the solutions?

Accepted Answer

$$x = 7$$ and $$x = -5$$

Question 2

Which of the following equations does NOT represent $$y as a $$function of $$x$$?

Accepted Answer

$$x = |y|$$

Question 3

Given $$f(x) = x^2$ - 4x + 2$$, find $$f(5).$$

Accepted Answer

$$f(5) = 13$$

Question 4

Which graph is symmetric with respect to the origin?

Accepted Answer

Graph I

Question 5

Solve the absolute value inequality $$|2x - 3| \u003c 8$$ and express the solution in interval notation.

Accepted Answer

$$(-2.5, 5.5)$$

Question 6

Find the inverse of the function $$f(x) = 12x + 3.$$

Accepted Answer

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

Question 7

Given $$g(x) = \sqrt{x - 5}$$, what is the domain of $$g(x) in $$interval notation?

Accepted Answer

$$[5, \infty)$$

Question 8

Which of the following is the correct solution to $$\sqrt{x + 3} - \sqrt{x - 4} = 3$$?

Accepted Answer

$$x = 12$$

Question 9

A population grows exponentially according to $$P(t) = 10,000e$$^{0.04t}$$, where t$ is years after 2015. Estimate the population in 2025.

Accepted Answer

$$P(10) \approx 14,918$$

Question 10

Which of the following is the correct interval notation for the solution to $$x^2 + 4x$$ \u003c 8$$?

Accepted Answer

$$(-6, 2)$$

Question 11

Express the variation: $$y$$ varies jointly as $$a$$ and $$m$$, and inversely as $$n. $$Which equation represents this?

Accepted Answer

$$y = k\frac{am}{n}$$

Question 12

Given $$f(x) = x^2$ + 2x$$, state the domain using set-builder notation.

Accepted Answer

$$\{x \mid x \in \mathbb{R}\}$$

Question 13

Write the logarithmic equation equivalent to $$e^{x+2} = 5$.

Accepted Answer

$$x + 2 = \ln 5$$

Question 14

If the half-life of a substance is 140 days, how many days will it take for a sample to decay to 20% of its original amount?

Accepted Answer

$$324$$ days

Question 15

Given $$f(x) = 2x^2$ - 4x + 3$$, use synthetic division to find $$f(2). $$What is the result?

Accepted Answer

$$f(2) = 3$$

Question 16

Simplify $$\log_{10} 1000.$$

Accepted Answer

$$3$$

Question 17

Which of the following is the correct equation for the circle with center $$(7, -1)$$ and radius $$9$$?

Accepted Answer

$$(x - 7)^2$ + (y + 1)^2$ = 81$$

Question 18

Given $$f(x) = 2^x$$, what is the equation of its inverse?

Accepted Answer

$$f^{-1}(x$$) = \$$log_2 x$

Question 19

Which of the following is the correct solution to $$x^2 - 10x$$ \u003c 8$$?

Accepted Answer

$$(5 - \sqrt{18}, 5 + \sqrt{18})$$

Comprehensive Study Guide: College Algebra Core Topics and Practice

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