Q: Which of the following systems of equations represents a situation where two lines are parallel and never intersect?

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

Question 1

Which of the following functions is continuous everywhere on $$\mathbb{R}$$?

Accepted Answer

$$f(x) = x^2$ + 3x - 5$$

Question 2

A piecewise-defined function is given by:

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

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

Accepted Answer

$$-1$$

Question 3

Which of the following is the graph of the greatest integer function $$f(x) = \lfloor x \rfloor$$?

Accepted Answer

A step function where each step is at integer values and the function jumps up at each integer.

Question 4

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

Accepted Answer

$$7$$

Question 5

Which transformation will shift the graph of $$f(x) = x^2$ two units to the right and three units up?

Accepted Answer

$$f(x) = (x-2)^2$ + 3$$

Question 6

Which of the following functions is even?

Accepted Answer

$$f(x) = x^2$

Question 7

Given $$f(x) = 2x - 1$$ and $$g(x) = x^2$, what is f(g(3$$))$$?

Accepted Answer

$$17$$

Question 8

The difference quotient for $$f(x) = x^2$ is $$\frac{f(x+h) - f(x)}{h}$$. What is its simplified form?

Accepted Answer

$$2x + h$$

Question 9

Which of the following systems of equations represents a situation where two lines are parallel and never intersect?

Accepted Answer

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

Question 10

Solve the system by substitution:

$$\begin{cases} x + y = 5 \ x - y = 1 \end{cases}$$

What is the solution?

Accepted Answer

$$(3, 2)$$

Question 11

A chemist mixes two solutions: one with 10% salt and one with 30% salt. If she wants 100 liters of a 20% salt solution, how many liters of each should she mix?

Accepted Answer

50 liters of each solution

Question 12

Which of the following is the domain of $$f(x) = \frac{1}{x-4}$$?

Accepted Answer

$$\mathbb{R} \setminus \{4\}$$

Question 13

Given $$f(x) = x^2$ and g(x$$) = \sqrt{x}$$, what is the domain of (f$$ \circ g)(x)$$?

Accepted Answer

$$x \geq 0$$

Question 14

Which of the following functions is odd?

Accepted Answer

$$f(x) = x^3$

Question 15

Solve the system of equations in three variables:

$$\begin{cases} x + y + z = 6 \ x - y + z = 2 \ x + y - z = 2 \end{cases}$$

What is the value of $$z$$?

Accepted Answer

$$2$$

Question 16

Which of the following inequalities represents the region above the line $$y = 2x - 1$$?

Accepted Answer

$$y \u003e 2x - 1$$

Question 17

A function $$f(x) is $$symmetric with respect to the origin if:

Accepted Answer

$$f(-x) = -f(x)$$

Question 18

If $$f(x) = |x|$$, which of the following statements is true?

Accepted Answer

$$f(x) is $$even

Question 19

Which of the following is the result of the composition $$(g \circ f)(x)$$, where $$f(x) = x+1$$ and $$g(x) = 2x$$?

Accepted Answer

$$2x + 2$$

Graphs, Functions, and Systems: Study Guide for College Algebra

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