$$\begin{bmatrix} 3 & 2 \\ 4 & 6 \end{bmatrix}$$

Question 1

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

Accepted Answer

It is defined for $$x \geq 0$$ and increases slowly as $$x$$ increases.

Question 2

Given the system of equations: $$\begin{cases} x + y = 4 \ x - y = 2 \end{cases}$$, what is the solution $$(x, y)$$?

Accepted Answer

$$(x, y) = (3, 1)$$

Question 3

Which of the following is the correct formula for the sum of the first $$n$$ natural numbers?

Accepted Answer

$$S = \dfrac{n(n+1)}{2}$$

Question 4

If $$A = \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix}$$ and $$B = \begin{bmatrix} 2 & 0 \ 1 & 2 \end{bmatrix}$$, what is $$A + B$$?

Accepted Answer

$$\begin{bmatrix} 3 & 2 \ 4 & 6 \end{bmatrix}$$

Question 5

Which of the following is the correct notation for the summation of $$x_i$$ from $$i=1 to$$ $$n$$?

Accepted Answer

$$\sum_{i=1}^{n} x_i$$

Question 6

Given the quadratic function $$f(x) = -x^2$ + 4x - 3$$, what is the vertex of the parabola?

Accepted Answer

$$(2, 1)$$

Question 7

Which of the following best describes the solution set of the equation $$|x| = 5$$?

Accepted Answer

$$x = 5 or$$ $$x = -5$$

Question 8

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 9

Which of the following graphs best represents a function that is increasing for all $$x in $$its domain?

Accepted Answer

A straight line with positive slope

Question 10

Given the data points $$(1,2), (2,4), (3,6), (4,8)$$, what type of relationship is best represented?

Accepted Answer

Linear

Question 11

If $$\sum_{i=1}^{4} i^2$ is calculated, what is the result?

Accepted Answer

$$30$$

Question 12

Which of the following is the solution to $$2x - 5 = 9$$?

Accepted Answer

$$x = 7$$

Question 13

If $$A = \begin{bmatrix} 1 & 0 \ 0 & 1 \end{bmatrix}$$, what is $$A$$ called?

Accepted Answer

Identity matrix

Question 14

Which of the following is the correct formula for the distance between two points $$(x_1$, y_1$)$$ and $$(x_2$, y_2$)$$?

Accepted Answer

$$\sqrt{(x_2$ - x_1$)^2$$ + ($$y_2$$ - $$y_1)^2$}$$

Question 15

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

Accepted Answer

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

Question 16

Which of the following is the correct formula for the slope of the line passing through points $$(x_1$, y_1$)$$ and $$(x_2$, y_2$)$$?

Accepted Answer

$$m = \dfrac{y_2$ - y_1$}{x_2$ - x_1$}$$

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

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