Q: If $f(x) = x^2$, what is the graph of $g(x) = (x-3)^2 + 2$ in relation to $f(x)$?

Shifted right 3 units and up 2 units

Q: Which transformation is applied to $f(x) = \sqrt{x}$ to obtain $g(x) = \sqrt{x+4} - 2$?

Shift left 4 units and down 2 units

Q: Which of the following best describes the symmetry of the function $f(x) = x^4$?

Even function; symmetric about the $y$-axis

Question 1

Given the quadratic equation $2x^2 - 4x + 3 = 0$, use the discriminant to determine the number and type of solutions.

Accepted Answer

Two complex (non-real) solutions

Question 2

Solve the quadratic equation $x^2 - 6x + 9 = 0$ and select the correct solution.

Accepted Answer

$x = 3$ (with multiplicity 2)

Question 3

A ball is thrown upward from the ground with an initial velocity of $20$ m/s. Its height $h$ (in meters) after $t$ seconds is given by $h(t) = -5t^2 + 20t$. When does the ball hit the ground again?

Accepted Answer

$t = 4$ seconds

Question 4

Given the function $f(x) = |x-2| + 1$, what is the vertex of its graph?

Accepted Answer

$(2, 1)$

Question 5

Which of the following functions is odd?

Accepted Answer

$f(x) = x^3$

Question 6

Given the piecewise function $f(x) = \begin{cases} x+2 & x < 0 \ 2x-1 & x \geq 0 \end{cases}$, what is $f(-3)$?

Accepted Answer

$-1$ (since $f(-3) = -3 + 2$)

Question 7

What is the equation of the line passing through the point $(1, 2)$ with slope $-3$ in point-slope form?

Accepted Answer

$y - 2 = -3(x - 1)$

Question 8

Find the equation of a line parallel to $y = 2x - 5$ that passes through $(0, 4)$.

Accepted Answer

$y = 2x + 4$

Question 9

If $f(x) = x^2$, what is the graph of $g(x) = (x-3)^2 + 2$ in relation to $f(x)$?

Accepted Answer

Shifted right 3 units and up 2 units

Question 10

Which transformation is applied to $f(x) = \sqrt{x}$ to obtain $g(x) = \sqrt{x+4} - 2$?

Accepted Answer

Shift left 4 units and down 2 units

Question 11

Find the inverse of the function $f(x) = 3x + 5$.

Accepted Answer

$f^{-1}(x) = \dfrac{x-5}{3}$

Question 12

What is the distance between the points $(2, -1)$ and $(-2, 3)$?

Accepted Answer

$2\sqrt{8}$

Question 13

Write the standard form of the equation of a circle with center $(3, -2)$ and radius $5$.

Accepted Answer

$(x-3)^2 + (y+2)^2 = 25$

Question 14

Given the function $f(x) = \dfrac{1}{x-4}$, what is its domain?

Accepted Answer

$x 
eq 4$

Question 15

Which of the following best describes the symmetry of the function $f(x) = x^4$?

Accepted Answer

Even function; symmetric about the $y$-axis

Question 16

A circle has the equation $x^2 + y^2 - 6x + 8y = 0$. What are its center and radius?

Accepted Answer

Center $(3, -4)$, radius $5$

Question 17

Given the function $f(x) = x^2 - 4x + 3$, what are its $x$-intercepts?

Accepted Answer

$x = 1$ and $x = 3$

Question 18

If a line has slope $\dfrac{1}{2}$, what is the slope of a line perpendicular to it?

Accepted Answer

$-2$

Question 19

What is the range of the function $f(x) = \sqrt{x-1}$?

Accepted Answer

$[0, \infty)$

Question 20

Given the function $f(x) = \begin{cases} 2x+1 & x < 1 \ x^2 & x \geq 1 \end{cases}$, what is $f(2)$?

Accepted Answer

$5$

College Algebra: Key Concepts and Methods Study Guide

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