Question 1

Given the function $f(x) = \sqrt{2x - 3}$, what is the domain of $f(x)$?

Accepted Answer

$x \geq 1.5$

Question 2

Solve for $x$: $5x - 2 = 3x + 6$

Accepted Answer

$x = 2$

Question 3

If $f(x) = 2x^2 - 5x + 3$, what is $f(-2)$?

Accepted Answer

$21$

Question 4

Which of the following is the solution set for $|x - 4| = 7$?

Accepted Answer

$x = -3$ and $x = 11$

Question 5

A car rental company charges a flat fee of $\$25$ plus $\$0.15$ per mile driven. If the total cost is $\$40$, how many miles were driven?

Accepted Answer

$75$

Question 6

Simplify: $\dfrac{2x^2 - 8}{x^2 - 4}$

Question 7

Which of the following is the solution to $\sqrt{x + 5} = 4$?

Accepted Answer

$x = 11$

Question 8

If $f(x) = 3x - 7$ and $g(x) = x^2$, what is $(f \circ g)(2)$?

Accepted Answer

$5$

Question 9

Solve for $x$: $\dfrac{x}{3} + 2 = 5$

Accepted Answer

$x = 9$

Question 10

Which of the following is the correct factorization of $x^2 - 9$?

Accepted Answer

$(x - 3)(x + 3)$

Question 11

A population of bacteria doubles every 3 hours. If the initial population is $500$, what will the population be after $9$ hours?

Accepted Answer

$4000$

Question 12

Solve for $x$: $2x^2 - 8x = 0$

Accepted Answer

$x = 0$ and $x = 4$

Question 13

Which of the following is the solution to $3(x - 2) = 2x + 5$?

Accepted Answer

$x = 7$

Question 14

If $f(x) = x^2 - 4x + 7$, what is the vertex of the parabola?

Accepted Answer

$(2, 3)$

Question 15

Which of the following is the solution set for $x^2 = 25$?

Accepted Answer

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

Question 16

A chemist mixes a solution that is $30\%$ acid with one that is $10\%$ acid to get $20$ liters of a $20\%$ acid solution. How many liters of the $30\%$ solution are used?

Accepted Answer

$10$

Question 17

Which of the following is the correct solution to $x^2 + 6x + 9 = 0$?

Accepted Answer

$x = -3$

Question 18

If $f(x) = 2x + 1$ and $g(x) = x - 3$, what is $f(g(4))$?

Accepted Answer

$3$

Question 19

Which of the following is the solution to $\dfrac{2x - 4}{x} = 0$?

Accepted Answer

$x = 2$

Question 20

A ball is thrown upward with an initial velocity of $32$ ft/s from a height of $48$ ft. Its height after $t$ seconds is given by $h(t) = -16t^2 + 32t + 48$. When does the ball reach its maximum height?

Accepted Answer

$t = 1$ s

Equations, Inequalities, and Functions: College Algebra Study Notes

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