Question 1

Which of the following relations is NOT a function?

Accepted Answer

The set of ordered pairs $$\{(1,2), (2,3), (3,4), (1,5)\}$$

Question 2

Given the function $$f(x) = \frac{2x+1}{x-3}$$, what is the domain in interval notation?

Accepted Answer

$$(-\infty, 3) \cup (3, \infty)$$

Question 3

A piecewise function is defined as $$f(x) = \begin{cases} x^2$ & x \u003c 0 \ 2x+1 & x \geq 0 \end{cases}. $$What is $$f(-2)$$?

Accepted Answer

$$4$$

Question 4

A population of bacteria grows according to $$P(t) = 500 \cdot 1.08^t. $$What is the average rate of change from $$t=0 to$$ $$t=3$$?

Accepted Answer

$$\frac{P(3) - P(0)}{3 - 0} = \frac{500 \cdot 1.08^3$ - 500}{3}$$

Question 5

Let $$f(x) = x^2$ and g(x) = x+1$. What is (f$$ \circ g)(2)$$?

Accepted Answer

$$9$$

Question 6

Which transformation describes $$y = -2f(x+3) - 4$$?

Accepted Answer

Reflect over x-axis, shift left 3, vertical stretch by 2, shift down 4

Question 7

Given $$f(x) = 2x - 5$$, find the inverse $$f^{-1}(x$$)$$.

Accepted Answer

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

Question 8

Solve the absolute value equation $$|3x - 2| = 7.$$

Accepted Answer

$$x = 3 or$$ $$x = -\frac{5}{3}$$

Question 9

What is the end behavior of $$f(x) = -2x^5$ + 3x^2$ - 7 as$$ $$x 	o \infty$$?

Accepted Answer

$$f(x) 	o -\infty$$

Question 10

Given $$f(x) = x^2$ - 4x + 7$$, find the vertex of the parabola.

Accepted Answer

$$(2, 3)$$

Question 11

For the polynomial $$f(x) = (x-2)^3$(x+1)^2$$, what happens at $$x = -1$?

Accepted Answer

The graph bounces at $$x = -1$$

Question 12

Find the difference quotient for $$f(x) = x^2$.

Accepted Answer

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

Question 13

Given $$f(x) = \frac{x^2$ - 9}{x - 3}$$, what type of discontinuity occurs at $$x = 3$$?

Accepted Answer

A hole (removable discontinuity)

Question 14

What is the horizontal asymptote of $$f(x) = \frac{4x^2$ + 1}{2x^2$ - 5}$$?

Accepted Answer

$$y = 2$$

Question 15

Solve for $$x$$: $$2^x = 16$$

Accepted Answer

$$x = 4$$

Question 16

Convert the exponential equation $$5^x = 125 to $$logarithmic form.

Accepted Answer

$$x = \log_5$(125)$$

Question 17

Expand $$\log_3$(9x^2$$)$ using log properties.

Accepted Answer

$$\log_3$(9) + 2\log_3$(x)$$

Question 18

A medication decays continuously at a rate of $$k = 0.05. $$What is the equivalent annual rate $$r$$?

Accepted Answer

$$r = e$$^{0.05}$$ - 1$$

Question 19

Solve the system: $$\begin{cases} x + y = 5 \ x - y = 1 \end{cases}$$

Accepted Answer

$$(3, 2)$$

MAT151 Final Exam Study Guide: College Algebra Essentials

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