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 $$3$$?

Accepted Answer

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 $$2x - 5 \u003e 3$$?

Accepted Answer

$$x \u003e 4$$

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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