Q: Which of the following is the determinant of the matrix $$\begin{pmatrix} 2 & 3 \\ 1 & 4 \end{pmatrix}$$?

$$2 \times 4 - 3 \times 1 = 5$$

Question 1

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

Accepted Answer

A curve that starts at $$(0,0)$$ and increases slowly, only defined for $$x \geq 0$$

Question 2

Given the set $$A = \{1, 2, 3\}$$ and $$B = \{2, 3, 4\}$$, what is $$A \cap B$$?

Accepted Answer

$$\{2, 3\}$$

Question 3

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 4

Which of the following is the solution set for $$|x - 3| = 5$$?

Accepted Answer

$$x = 8 or$$ $$x = -2$$

Question 5

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

Accepted Answer

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

Question 6

Which of the following represents the sum $$\sum_{i=1}^{4} i^2$?

Accepted Answer

$$1^2$$ + $$2^2$$ + $$3^2$$ + $$4^2 = 30$

Question 7

If $$A = \begin{pmatrix} 1 & 2 \ 3 & 4 \end{pmatrix}$$ and $$B = \begin{pmatrix} 2 & 0 \ 1 & 2 \end{pmatrix}$$, what is the $$(1,2)$$ entry of $$A + B$$?

Accepted Answer

$$4$$

Question 8

Which of the following is the domain of the function $$f(x) = \frac{1}{x-2}$$?

Accepted Answer

$$x 
eq 2$$

Question 9

A real-world application: A company’s profit $$P (in $$thousands of dollars) is modeled by $$P(x) = -2x^2$ + 8x + 10$$, 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 $$18 at$$ $$x = 2$$

Question 10

Which of the following is the solution to the system of equations: $$\begin{cases} x + y = 5 \ x - y = 1 \end{cases}$$?

Accepted Answer

$$(x, y) = (3, 2)$$

Question 11

Which of the following is the correct simplification of $$\sqrt{50}$$?

Accepted Answer

$$5\sqrt{2}$$

Question 12

Given the scatter plot of a set of data points that form a roughly upward trend, which type of correlation is most likely present?

Accepted Answer

Positive correlation

Question 13

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

Accepted Answer

$$f(3) = 9$$

Question 14

Which of the following is the range of the function $$f(x) = x^2$ for x$$ \in \mathbb{R}$$?

Accepted Answer

$$[0, \infty)$$

Question 15

If $$A = \{1, 2, 3, 4\}$$ and $$B = \{3, 4, 5, 6\}$$, what is $$A \cup B$$?

Accepted Answer

$$\{1, 2, 3, 4, 5, 6\}$$

Question 16

Which of the following is the solution to $$2x^2 - 8 = 0$?

Accepted Answer

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

Question 17

If $$f(x) = 3x - 7$$, what is the inverse function $$f^{-1}(x$$)$$?

Accepted Answer

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

Question 18

Which of the following is the determinant of the matrix $$\begin{pmatrix} 2 & 3 \ 1 & 4 \end{pmatrix}$$?

Accepted Answer

$$2 	imes 4 - 3 	imes 1 = 5$$

Question 19

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

Accepted Answer

$$22$$ meters at $$t = 2$$ seconds

Key Concepts in College Algebra: Functions, Graphs, Matrices, and Series

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