Question 1

Given the points $$A(2, -3)$$ and $$B(-4, 5)$$, what is the distance between $$A$$ and $$B$$?

Accepted Answer

$$\sqrt{52}$$

Question 2

Which of the following is the correct equation for the inverse of the function $$f(x) = 3x + 7$$?

Accepted Answer

$$f^{-1}(x$$) = \dfrac{x - 7}{3}$$

Question 3

A population of bacteria triples every 4 hours. If the initial population is 200, which equation models the population $$P$$ after $$t$$ hours?

Accepted Answer

$$P = 200 \cdot 3$$^{t/4}$$

Question 4

Which of the following functions is even?

Accepted Answer

$$f(x) = x^2$ + 1$$

Question 5

Solve the inequality $$2x - 5 \u003e 7.$$

Accepted Answer

$$x \u003e 6$$

Question 6

What is the domain of the function $$f(x) = \sqrt{5 - x}$$?

Accepted Answer

$$(-\infty, 5]$$

Question 7

If $$f(x) = x^2$ and g(x) = x + 1$, what is (f$$ \circ g)(2)$$?

Accepted Answer

$$9$$

Question 8

Which of the following is the $$y-$$intercept of the function $$f(x) = 2x^2$ - 3x + 5$$?

Accepted Answer

$$(0, 5)$$

Question 9

A company’s revenue $$R (in $$thousands of dollars) is modeled by $$R(x) = 50x - x^2$, where x$ is the number of units sold (in thousands). What is the maximum revenue?

Accepted Answer

$$625$$ thousand dollars

Question 10

Which transformation maps the graph of $$y = f(x) to$$ $$y = f(x - 4) + 2$$?

Accepted Answer

Right 4 units, up 2 units

Question 11

Solve the system of equations: $$\begin{cases} 2x + y = 7 \ x - y = 1 \end{cases}$$

Accepted Answer

$$x = 2,\ y = 3$$

Question 12

Which of the following is the solution to $$\log_2$(x) = 5$$?

Accepted Answer

$$x = 32$$

Question 13

Find the midpoint of the segment joining $$(-6, 2)$$ and $$(4, -8).$$

Accepted Answer

$$( -1, -3 )$$

Question 14

Which of the following is the range of the function $$f(x) = 2^x$$?

Accepted Answer

$$(0, \infty)$$

Question 15

If $$f(x) = \ln(x)$$, what is the domain of $$f$$?

Accepted Answer

$$(0, \infty)$$

Question 16

Which of the following is the $$x-$$intercept of the function $$f(x) = x^2$ - 9$$?

Accepted Answer

$$(-3, 0)$$ and $$(3, 0)$$

Question 17

Solve the quadratic equation $$x^2 - 6x + 5 = 0$.

Accepted Answer

$$x = 1$$ and $$x = 5$$

Question 18

Which of the following is the correct simplification of $$\log_{10}(1000)$$?

Accepted Answer

$$3$$

Question 19

A medication decays in the bloodstream according to $$C(t) = 50e$$^{-0.2t}$$, where C$ is the concentration in mg/L and t$ is time in hours. What is the concentration after 5 hours?

Accepted Answer

$$18.4 mg/L$$

Comprehensive Study Guide: College Algebra Final Exam Topics (Units 1-3)

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