$$ x \geq 0 $$ and $$ x \neq 1 $$

Question 1

Given the equation of a circle $$ (x + 5)^2$ + (y + 9.5)^2$ = 30.25 $$, what is the center and radius of the circle?

Accepted Answer

Center: $$ (-5, -9.5) $$, Radius: $$ 5.5 $$

Question 2

Solve the inequality $$ -24 \u003c 2x + 18 \leq 12 $$ and choose the correct solution set.

Accepted Answer

$$ -21 \u003c x \leq -3 $$

Question 3

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

Accepted Answer

$$ x \geq 0 $$

Question 4

Find the equation of the line parallel to $$ y = 2x - 3 $$ passing through $$ (-1, 3) .$$

Accepted Answer

$$ y = 2x + 1 $$

Question 5

Find the equation of the line perpendicular to $$ y = x $$ passing through $$ (-2, 4) .$$

Accepted Answer

$$ y = -x + 2 $$

Question 6

Given $$ f(x) = \sqrt{2 - 3x} $$ and $$ g(x) = x^2$ - 3x + 2 $$, find $$ (f + g)(-2) .$$

Accepted Answer

$$ 10 $$

Question 7

Solve the system of equations: $$ -4x + 3y = 17 $$ and $$ 5x + 2y = 27 . $$What is the solution?

Accepted Answer

$$ (3, 5) $$

Question 8

What is the domain of $$ f(x) = \frac{1}{1 - x} $$?

Accepted Answer

$$ x 
eq 1 $$

Question 9

A chemical reaction is modeled by $$ f(x) = 12x^2$ - 300 . $$What is the domain of this function?

Accepted Answer

$$ x \in \mathbb{R} $$

Question 10

Given $$ f(x) = \sqrt{x - 9} $$ and $$ g(x) = x^2$ - 3x + 2 $$, what is the domain of $$ f(x) $$?

Accepted Answer

$$ x \geq 9 $$

Question 11

A medical dosage is modeled by $$ f(x) = \frac{\sqrt{x}}{1 - x} . $$What is the domain of $$ f(x) $$?

Accepted Answer

$$ x \geq 0 $$ and $$ x 
eq 1 $$

Question 12

If $$ y - 5 = 1.5(x + 2) $$, what is the slope and y-intercept of the line?

Accepted Answer

Slope: $$ 1.5 $$, y-intercept: $$ 8 $$

Question 13

Which of the following is the correct standard form for the line $$ y = -2x + 4 $$?

Accepted Answer

$$ 2x + y = 4 $$

Question 14

Given $$ f(x) = \sqrt{2 - 3x} $$ and $$ g(x) = x^2$ - 3x + 2 $$, find $$ (f \circ g)(-5) .$$

Accepted Answer

$$ \sqrt{2 - 3((-5)^2$ - 3(-5) + 2)} $$

Question 15

If two lines are perpendicular and one has slope $$ m $$, what is the slope of the other?

Accepted Answer

$$ -\frac{1}{m} $$

Question 16

Solve the inequality $$ 25x - 4 \geq 7x - 40 .$$

Accepted Answer

$$ x \geq -2 $$

Question 17

A historical event is modeled by $$ f(x) = 3\sqrt{x - 9} . $$What is the domain of $$ f(x) $$?

Accepted Answer

$$ x \geq 9 $$

Question 18

Given $$ f(x) = \sqrt{2 - 3x} $$ and $$ g(x) = x^2$ - 3x + 2 $$, find $$ (g \circ f)(-1) .$$

Accepted Answer

$$ (\sqrt{2 - 3(-1)})^2$ - 3\sqrt{2 - 3(-1)} + 2 $$

Question 19

Which of the following is the correct point-slope form for a line with slope $$ m $$ passing through $$ (x_1$, y_1$) $$?

Accepted Answer

$$ y = m(x - x_1$) + y_1$ $$

College Algebra Exam I Review – Step-by-Step Guidance

Study Guide - Practice Questions