Question 1

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

Accepted Answer

A function that can be written in the form $$f(x) = a_n x^n + a_{n-1} x$$^{n-1}$$ + \ldots + a_1$ x + a_0$, where all coefficients a_i$ are real numbers and n$ is a non-negative integer.

Question 2

A pharmaceutical company models the concentration of a drug in the bloodstream over time with the function $$C(t) = 50e$$^{-0.2t}$$, where C$ is in mg/L and t$ is in hours. What type of function is this, and what is its domain?

Accepted Answer

Exponential function; domain is all real numbers $$t \geq 0$$

Question 3

Which of the following equations represents a rational inequality?

Accepted Answer

$$\displaystyle \frac{x+2}{x-3} \u003e 0$$

Question 4

Given the piecewise function

$$\displaystyle f(x) = \begin{cases} x^2$, & x \u003c 0 \ 2x + 1, & x \geq 0 \end{cases}$$

What is $$f(-3) + f(2)$$?

Accepted Answer

$$9 + 5 = 14$$

Question 5

A company’s profit $$P (in $$thousands of dollars) is modeled by $$P(x) = -2x^2$ + 12x - 9$$, where $$x is $$the number of units sold (in thousands). What is the maximum profit, and for how many units sold does it occur?

Accepted Answer

Maximum profit is $$15$$ thousand dollars at $$x = 3$$ thousand units.

Question 6

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

Accepted Answer

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

Question 7

Solve the following system of equations using matrices:

$$\begin{cases} 2x + 3y = 7 \ x - y = 1 \end{cases}$$

Accepted Answer

$$x = 2,\ y = 1$$

Question 8

Which of the following best describes the domain of the function $$f(x) = \sqrt{5 - x}$$?

Accepted Answer

$$x \leq 5$$

Question 9

A population of bacteria triples every 4 hours. If the initial population is 200, which equation models the population $$P$$ after $$t$$ hours?

Accepted Answer

$$P = 200 \cdot 3$$^{t/4}$$

Question 10

Which of the following is the solution set for the inequality $$|2x - 5| \u003c 7$$?

Accepted Answer

$$-1 \u003c x \u003c 6$$

Question 11

Given $$f(x) = x^2$ - 4$$ and $$g(x) = x + 2$$, what is $$(f \circ g)(3)$$?

Accepted Answer

$$21$$

Question 12

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

Accepted Answer

$$x = 32$$

Question 13

A quadratic equation $$ax^2 + bx + c = 0$ has real and distinct roots if:

Accepted Answer

$$b^2 - 4ac$$ \u003e 0$$

Question 14

Which of the following is the sum of the first 5 terms of the arithmetic sequence where $$a_1 = 3$ and d = 4$?

Accepted Answer

$$55$$

Question 15

A conic section is defined by the equation $$x^2$$ + $$4y^2 = 16$. What type of conic is this, and what are its axes lengths?

Accepted Answer

Ellipse; axes lengths are $$4$$ and $$2$$

Question 16

A student invests $$\1000$ in an account that earns 6$$\%$$ annual interest compounded quarterly. Which formula gives the amount A$ after t$ years?

Accepted Answer

$$A = 1000 \left(1 + \frac{0.06}{4}\$$right)^{4t}$$

Question 17

Which of the following is the correct domain for the function $$f(x) = \displaystyle \frac{2x+1}{x^2$ - 9}$$?

Accepted Answer

$$x 
eq 3,\ x 
eq -3$$

Question 18

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

Accepted Answer

$$7$$

Question 19

A lottery has 5 winning tickets out of 1000. What is the probability of buying a single ticket and winning?

Accepted Answer

$$\displaystyle \frac{1}{200}$$

College Algebra Syllabus and Course Overview – MATH 1314

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