Question 1

Which of the following best describes the domain of the function $$f(x) = \sqrt{x-3}$$?

Accepted Answer

$$[3, \infty)$$

Question 2

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

Accepted Answer

$$2x^2 + 1$

Question 3

Which of the following equations represents a circle in the $$xy-$$plane?

Accepted Answer

$$x^2$$ + $$y^2 = 16$

Question 4

Solve for $$x$$: $$2^{x+1} = 16$.

Accepted Answer

$$x = 3$$

Question 5

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

Accepted Answer

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

Question 6

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 7

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

Accepted Answer

$$x = 32$$

Question 8

If $$f(x) = x^2$ - 4x + 3$$, what are the zeros of $$f(x)$$?

Accepted Answer

$$x = 3$$ and $$x = 1$$

Question 9

Which of the following systems of equations can be solved using matrices?

Accepted Answer

$$x + y = 5,\ 2x - y = 1$$

Question 10

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

$$35$$

Question 11

Which of the following is the correct factorization of $$x^3 - 8$?

Accepted Answer

$$(x - 2)(x^2$ + 2x + 4)$$

Question 12

A company’s revenue $$R (in $$thousands of dollars) is modeled by $$R(x) = -2x^2$ + 12x + 20$$, where $$x is $$the number of units sold (in thousands). What is the maximum revenue?

Accepted Answer

$$R = 56$$

Question 13

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

Accepted Answer

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

Question 14

Which of the following is the correct solution to the equation $$\frac{1}{x} + \frac{1}{x+2} = 1$$?

Accepted Answer

$$x = -1 \pm \sqrt{2}$$

Question 15

If $$f(x) = 2x^2$ - 8x + 6$$, what is the vertex of the parabola?

Accepted Answer

$$(2, -2)$$

Question 16

Which of the following is the sum of the infinite geometric series $$3 + 1.5 + 0.75 + \ldots$$?

Accepted Answer

$$6$$

Question 17

Which of the following is the correct solution to the equation $$\log_{10}(x^2$ - 4) = 1$$?

Accepted Answer

$$x = \pm 4$$

Question 18

A quadratic function models the height $$h (in $$meters) of a ball $$t$$ seconds after it is thrown: $$h(t) = -5t^2$ + 20t + 2. $$What is the maximum height reached by the ball?

Accepted Answer

$$22$$ meters

Question 19

Which of the following is the correct solution to the system of equations: $$\begin{cases} 2x + 3y = 7 \ x - y = 1 \end{cases}$$?

Accepted Answer

$$x = 2, y = 1$$

College Algebra Syllabus and Course Overview – Dallas College MATH 1314

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