$$\begin{pmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{pmatrix}$$

$$\begin{pmatrix} 4 & 4 \\ 10 & 8 \end{pmatrix}$$

Question 1

Which of the following is an irrational number?

Accepted Answer

$$\sqrt{2}$$

Question 2

What is the solution to the equation $$2x^2 - 8x + 6 = 0$?

Accepted Answer

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

Question 3

Which property of equality is used when you add the same number to both sides of an equation?

Accepted Answer

Addition Property of Equality

Question 4

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

Accepted Answer

$$2x^2 + 3$

Question 5

What is the vertex of the quadratic function $$y = -3(x - 2)^2$ + 5$$?

Accepted Answer

$$(2, 5)$$

Question 6

Which of the following matrices is a $$2 	imes 3$$ matrix?

Accepted Answer

$$\begin{pmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \end{pmatrix}$$

Question 7

What is the result of $$i^4$$ where $$i is $$the imaginary unit?

Accepted Answer

$$1$$

Question 8

Which of the following is the domain of the function $$f(x) = \frac{1}{x-3}$$?

Accepted Answer

$$\{ x \mid x 
eq 3 \}$$

Question 9

Solve the exponential equation $$2^{x} = 16$.

Accepted Answer

$$x = 4$$

Question 10

What is the midpoint between the points $$(1, 4)$$ and $$(5, 8)$$?

Accepted Answer

$$(3, 6)$$

Question 11

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

Accepted Answer

$$-3 \u003c x \u003c 7$$

Question 12

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

Accepted Answer

$$(x + 1)^2$

Question 13

What is the distance between the points $$(2, 3)$$ and $$(5, 7)$$?

Accepted Answer

$$5$$

Question 14

Which of the following is a one-to-one function?

Accepted Answer

$$f(x) = 2x + 1$$

Question 15

What is the solution to the logarithmic equation $$\log_{2}(x) = 3$$?

Accepted Answer

$$x = 8$$

Question 16

Which of the following is the range of the function $$f(x) = x^2$?

Accepted Answer

$$\{ y \mid y \geq 0 \}$$

Question 17

What is the result of multiplying the matrices $$\begin{pmatrix} 1 & 2 \ 3 & 4 \end{pmatrix}$$ and $$\begin{pmatrix} 2 & 0 \ 1 & 2 \end{pmatrix}$$?

Accepted Answer

$$\begin{pmatrix} 4 & 4 \ 10 & 8 \end{pmatrix}$$

Question 18

Which exponent rule is used to simplify $$x^3$$ \cdot $$x^4$$?

Accepted Answer

Product of Powers Rule: $$x^m \cdot x^n = x$$^{m+n}$$

Question 19

A baseball's height is modeled by $$h(t) = -16t^2$ + 64t + 5. $$What is the maximum height reached by the baseball?

Accepted Answer

$$69$$ feet

MAT 111 Final Exam Review: Comprehensive Study Notes for College Algebra

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