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

$$f(g(2)) = 2 \times 4 + 1 = 9$$

Question 1

Which of the following is the correct solution to the equation $$3x + 10 = 4$$?

Accepted Answer

$$x = -2$$

Question 2

Which of the following expressions is equivalent to $$a^2$$ - $$b^2$$?

Accepted Answer

$$(a + b)(a - b)$$

Question 3

A chemist is mixing two solutions, one with a concentration of $$x$$% and another with $$y$$%. If the final mixture is twice as much as the first solution and three times as much as the second, which equation represents the total amount of the mixture?

Accepted Answer

$$2x + 3y = 	ext{total mixture}$$

Question 4

Which of the following is the correct factorization of $$x^2 - 5x + 6$?

Accepted Answer

$$(x - 2)(x - 3)$$

Question 5

A population of bacteria doubles every 3 hours. If the initial population is $$P_0$$, which equation models the population after $$t$$ hours?

Accepted Answer

$$P(t) = P_0$ \cdot 2$$^{t/3}$$

Question 6

Which of the following is the solution to the inequality $$2x - 5 \u003c 7$$?

Accepted Answer

$$x \u003c 6$$

Question 7

Given the function $$f(x) = x^2$ - 4x + 3$$, what is the $$y-$$intercept?

Accepted Answer

$$(0, 3)$$

Question 8

A medical researcher is tracking the decay of a drug in the bloodstream, modeled by $$C(t) = C_0$ e$$^{-kt}$$. If C_0$ = 100 mg $$and $$k = 0.2$$, what is the concentration after 5 hours?

Accepted Answer

$$C(5) = 100 e$$^{-1}$$

Question 9

Which of the following is the correct solution to $$\frac{2}{3x - 1} = \frac{7}{3x - 1}$$?

Accepted Answer

No solution

Question 10

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

Accepted Answer

$$f(g(2)) = 2 	imes 4 + 1 = 9$$

Question 11

Which of the following is the correct algebraic expression for: 'Twice $$x is $$equal to 3 less than half $$x$$'?

Accepted Answer

$$2x = \frac{1}{2}x - 3$$

Question 12

Which of the following is the correct solution to the equation $$x^2 = 16$?

Accepted Answer

$$x = \pm 4$$

Question 13

A company’s revenue $$R is $$given by $$R = 50x - x^2$, where x$ is the number of units sold. What number of units maximizes the revenue?

Accepted Answer

$$x = 25$$

Question 14

Which of the following is the correct solution to the system of equations: $$x + y = 5$$ and $$x - y = 1$$?

Accepted Answer

$$x = 3, y = 2$$

Question 15

Which of the following is the correct domain of the function $$f(x) = \frac{1}{x - 2}$$?

Accepted Answer

$$x 
eq 2$$

Question 16

A radioactive substance decays according to $$A(t) = A_0$ e$$^{-0.1t}$$. If A_0$ = 200$$ grams, how much remains after 10 hours?

Accepted Answer

$$A(10) = 200 e$$^{-1}$$

Question 17

Which of the following is the correct solution to $$\log_2$(x) = 3$$?

Accepted Answer

$$x = 8$$

Question 18

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

Accepted Answer

$$f(2) + g(2) = 4 + 3 = 7$$

Question 19

Which of the following is the correct solution to the quadratic equation $$x^2 + 4x + 4 = 0$?

Accepted Answer

$$x = -2$$

Question 20

A car depreciates in value by 20% each year. If its initial value is $$V_0$$, what is its value after $$t$$ years?

Accepted Answer

$$V(t) = V_0$ \cdot 0.8^t$$

MATH 206: Algebra & Functions – Syllabus and Study Guide

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