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

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 $|2x - 3| < 8$ 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 $x^2 + 4x < 8$?

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 $x^2 - 10x < 8$?

Accepted Answer

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

Comprehensive Study Guide: College Algebra Core Topics and Practice

Study Guide - Practice Questions