Q: A car depreciates in value by $15\%$ each year. If the car is currently worth $\$20,000$, what will its value be after $2$ years?

$20,000 \times 0.85^2 = \$14,450$

Q: A medical test result is modeled by the function $T(x) = 0.5x^2 - 3x + 7$, where $x$ is the number of days after treatment. What is the minimum value of $T(x)$?

$T(3) = 0.5 \times 9 - 3 \times 3 + 7 = 4.5 - 9 + 7 = 2.5$

Question 1

Which of the following is the correct equation of a line passing through the point $(2, 0)$ with a slope of $3$?

Question 2

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

Accepted Answer

$(1, 0)$

Question 3

If the equation of a circle is $$(x - 2)^2 + (y + 3)^2 = 16$$, what is the center and radius of the circle?

Accepted Answer

Center: $(2, -3)$, Radius: $4$

Question 4

A chemical reaction's rate is modeled by the function $R(t) = 5e^{-0.2t}$, where $t$ is time in minutes. What is the rate after $10$ minutes?

Accepted Answer

$R(10) = 5e^{-2} \approx 0.676$

Question 5

Which of the following is the solution set for the inequality $2x - 5 > 3$?

Accepted Answer

$x > 4$

Question 6

A population of bacteria doubles every $3$ hours. If the initial population is $100$, which function models the population $P(t)$ after $t$ hours?

Accepted Answer

$P(t) = 100 \cdot 2^{t/3}$

Question 7

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

Accepted Answer

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

Question 8

A projectile is launched from the ground with an initial velocity of $20$ m/s. Its height $h$ in meters after $t$ seconds is given by $h(t) = -4.9t^2 + 20t$. At what time does the projectile reach its maximum height?

Accepted Answer

$t = 2.04$ seconds

Question 9

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

Accepted Answer

$x = 1$

Question 10

Which of the following is the domain of the function $f(x) = \frac{1}{x-2}$?

Accepted Answer

$x 
eq 2$

Question 11

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

Accepted Answer

$f(g(2)) = 2 \cdot 4 + 1 = 9$

Question 12

A car depreciates in value by $15\%$ each year. If the car is currently worth $\$20,000$, what will its value be after $2$ years?

Accepted Answer

$20,000 	imes 0.85^2 = \$14,450$

Question 13

Which of the following is the solution to the quadratic equation $x^2 - 4x + 3 = 0$?

Accepted Answer

$x = 1$ or $x = 3$

Question 14

A medical test result is modeled by the function $T(x) = 0.5x^2 - 3x + 7$, where $x$ is the number of days after treatment. What is the minimum value of $T(x)$?

Accepted Answer

$T(3) = 0.5 	imes 9 - 3 	imes 3 + 7 = 4.5 - 9 + 7 = 2.5$

Question 15

Which of the following is the solution to the system of equations: $\begin{cases} x + y = 5 \ x - y = 1 \end{cases}$?

Accepted Answer

$(3, 2)$

Question 16

If $f(x) = \sqrt{x-1}$, what is the domain of $f$?

Accepted Answer

$x \geq 1$

Question 17

A rectangle has a length that is $3$ units more than twice its width. If the area is $30$ square units, what is the width?

Accepted Answer

$3$

Question 18

Which of the following is the solution to $\log_2(x) = 5$?

Accepted Answer

$x = 32$

Question 19

If $y$ varies directly as $x$ and $y = 10$ when $x = 2$, what is the value of $y$ when $x = 5$?

Accepted Answer

$y = 25$

Question 20

A quadratic function models the height of a ball thrown upward: $h(t) = -16t^2 + 32t + 5$. What is the maximum height reached by the ball?

Accepted Answer

$37$ units

Graphing and Analyzing Functions in College Algebra

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