Q: Determine the domain and range for the relation $\{(3,3), (1,-1), (8,-3), (1,6)\}$.

Domain: $\{1, 3, 8\}$, Range: $\{-1, 3, -3, 6\}$

Q: Given $y = -2x + 4$, identify the slope and $y$-intercept, then sketch the graph.

Slope: $-2$, $y$-intercept: $4$

Q: If the length of a rectangle is $3$ units less than twice the width, and the perimeter is $18$ units, what are the dimensions of the rectangle?

Width: $3$ units, Length: $6$ units

Q: Solve for $x$ in the equation $2x - 5 = 3x + 2$ and interpret the solution in the context of a real-world scenario where $x$ represents the number of years until two investments are equal in value.

$x = -7$, so the investments will never be equal in the future.

Question 1

Solve the equation $5x - 7 = 2x + 8$ for $x$.

Accepted Answer

$x = 5$

Question 2

Express the solution set of $-3 < 4x + 1 \leq 9$ in interval notation.

Accepted Answer

$(-1, 2]$

Question 3

Solve for $x$ in the equation $2(x - 5) = 3x + 2$.

Accepted Answer

$x = -2$

Question 4

Determine the domain and range for the relation $\{(3,3), (1,-1), (8,-3), (1,6)\}$.

Accepted Answer

Domain: $\{1, 3, 8\}$, Range: $\{-1, 3, -3, 6\}$

Question 5

Given $y = -2x + 4$, identify the slope and $y$-intercept, then sketch the graph.

Accepted Answer

Slope: $-2$, $y$-intercept: $4$

Question 6

A savings account is started at $1000$ dollars with an interest rate of $5\%$ per year, compounded annually. What will the balance be after $3$ years? (Round to the nearest dollar)

Accepted Answer

$1158$

Question 7

A customer pays $34.40$ for $5$ items, some at $5.00$ each and some at $8.00$ each. How many of each item did the customer buy?

Accepted Answer

$2$ at $5.00$, $3$ at $8.00$

Question 8

Solve the system of equations: $2x + 3y = 10$ and $x - y = 1$.

Accepted Answer

$x = 3, y = 2$

Question 9

If the length of a rectangle is $3$ units less than twice the width, and the perimeter is $18$ units, what are the dimensions of the rectangle?

Accepted Answer

Width: $3$ units, Length: $6$ units

Question 10

Solve the quadratic equation $x^2 - 4x + 1 = 0$.

Accepted Answer

$x = 2 \pm \sqrt{3}$

Question 11

Which of the following is the solution to the inequality $2x - 5 > 3x + 2$?

Accepted Answer

$x < -7$

Question 12

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

Accepted Answer

$(2, 3)$

Question 13

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

Accepted Answer

$x = -7$

Question 14

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

Accepted Answer

$9$

Question 15

Solve the equation $2x - 5 = 3x + 2$ for $x$.

Accepted Answer

$x = -7$

Question 16

Which of the following intervals represents the solution to $-3 < 4x + 1 \leq 9$?

Accepted Answer

$(-1, 2]$

Question 17

If $f(x) = 2x - 5$, what is $f^{-1}(x)$, the inverse function?

Accepted Answer

$f^{-1}(x) = \frac{x+5}{2}$

Question 18

Solve for $x$ in the equation $2x - 5 = 3x + 2$ and interpret the solution in the context of a real-world scenario where $x$ represents the number of years until two investments are equal in value.

Accepted Answer

$x = -7$, so the investments will never be equal in the future.

Key Concepts and Problem Types in College Algebra: Equations, Inequalities, Functions, and Applications

Study Guide - Practice Questions

Study Guide - Flashcards