Q: Which of the following describes the end behavior of the polynomial $$f(x) = -3x^4$ + 2x^2$ - 7$$?

As $$x \to \infty$$, $$f(x) \to -\infty$$; as $$x \to -\infty$$, $$f(x) \to -\infty$$

Q: Given $$f(x) = \frac{1}{x-2}$$, what is the domain of $$f$$?

All real numbers $$x$$ such that $$x \neq 2$$

Q: A medical researcher uses the function $$T(x) = 98.6 + 0.5x to $$model a patient's temperature after $$x$$ hours of exercise. What is the patient's temperature after 4 hours?

$$T(4) = 98.6 + 0.5 \times 4 = 100.6$$

Question 1

Which of the following is the correct definition of a function?

Accepted Answer

A relation where each input is paired with exactly one output.

Question 2

Given the function $$f(x) = 2x^2$ - 3x + 5$$, what is the domain of $$f$$?

Accepted Answer

All real numbers $$x$$

Question 3

A pharmaceutical company models the concentration of a drug in the bloodstream over time with $$C(t) = 50e$$^{-0.2t}$$, where t$ is in hours. What is the concentration after 3 hours?

Accepted Answer

$$C(3) = 50e$$^{-0.6}$$ \approx 27.4$$

Question 4

Which of the following describes the end behavior of the polynomial $$f(x) = -3x^4$ + 2x^2$ - 7$$?

Accepted Answer

As $$x 	o \infty$$, $$f(x) 	o -\infty$$; as $$x 	o -\infty$$, $$f(x) 	o -\infty$$

Question 5

If $$f(x) = x^2$ + 1$$ and $$g(x) = 2x - 3$$, what is $$(f \circ g)(x)$$?

Accepted Answer

$$(f \circ g)(x) = (2x - 3)^2$ + 1$$

Question 6

A population of bacteria doubles every 4 hours. If the initial population is 500, which equation models the population $$P$$ after $$t$$ hours?

Accepted Answer

$$P(t) = 500 \cdot 2$$^{t/4}$$

Question 7

Solve the absolute value equation: $$|2x - 5| = 9$$

Accepted Answer

$$x = 7 or$$ $$x = -2$$

Question 8

Which transformation occurs when the graph of $$f(x) = x^2$ is changed to g(x) = (x$$ - $$3)^2 + 4$?

Accepted Answer

Shift right 3 units and up 4 units

Question 9

Given $$f(x) = \frac{1}{x-2}$$, what is the domain of $$f$$?

Accepted Answer

All real numbers $$x$$ such that $$x 
eq 2$$

Question 10

A chemical reaction is modeled by $$A(t) = 100e$$^{-0.05t}$$, where A$ is the amount of reactant left after t$ minutes. How long will it take for only 50 units of reactant to remain?

Accepted Answer

$$t = \frac{\ln(2)}{0.05} \approx 13.86$$ minutes

Question 11

Which of the following is the inverse function of $$f(x) = 3x + 7$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x - 7}{3}$$

Question 12

Solve the system of equations: $$\begin{cases} x + y + z = 6 \ 2x - y + 3z = 14 \ x - 2y + z = 2 \end{cases}$$

Accepted Answer

$$x = 3, y = 1, z = 2$$

Question 13

Which property of logarithms allows you to write $$\log_b(xy) as$$ $$\log_b(x) + \log_b(y)$$?

Accepted Answer

Product property

Question 14

A rational function $$f(x) = \frac{2x+1}{x-4}$$ has a vertical asymptote at:

Accepted Answer

$$x = 4$$

Question 15

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

Accepted Answer

All real numbers $$x$$ such that $$x \geq 1$$

Question 16

A medical researcher uses the function $$T(x) = 98.6 + 0.5x to $$model a patient's temperature after $$x$$ hours of exercise. What is the patient's temperature after 4 hours?

Accepted Answer

$$T(4) = 98.6 + 0.5 	imes 4 = 100.6$$

Question 17

Which of the following is the correct solution to the inequality $$2x - 7 \u003c 5$$?

Accepted Answer

$$x \u003c 6$$

Question 18

Convert the exponential equation $$3^x = 81 to $$logarithmic form and solve for $$x.$$

Accepted Answer

$$x = \log_3$(81) = 4$$

Question 19

Which of the following describes the graph of $$f(x) = -x^2$ compared to f(x$$) = $$x^2$$?

Accepted Answer

It is reflected over the $$x-$$axis.

MAC 1105 College Algebra Syllabus and Course Structure Study Guide

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