Q: Which of the following is the equation of the piecewise-defined function graphed in image 3?

$$f(x) = \begin{cases} -x - 4 & x \leq -3 \\ 2x + 3 & x \u003e -3 \end{cases}$$

Question 1

Solve for $$x$$: $$\frac{5}{2}x - 7 = 3.$$

Accepted Answer

Question 2

Solve the inequality and express the solution in interval notation: $$\frac{3}{2}x + 4 \geq 20.$$

Accepted Answer

$$x \geq 12$$

Question 3

Determine the domain of the function $$f(x) = \sqrt{x + 3}.$$

Accepted Answer

$$[-3, \infty)$$

Question 4

Given the function $$f(x) = \frac{x^2$ + 5x}{x^2$ + x - 42}$$, what is the domain?

Accepted Answer

$$(-\infty, -7) \cup (-7, 6) \cup (6, \infty)$$

Question 5

For the graph shown in image 1, what is the domain and range?

Accepted Answer

Domain: $$[-4, \infty)$$, Range: $$[-1, \infty)$$

Question 6

Which of the following functions is odd?

Accepted Answer

$$f(x) = x^3$ - 4x$$

Question 7

Find and simplify the difference quotient for $$f(x) = 3x^2$ + 2.$$

Accepted Answer

$$6x + 3h$$

Question 8

Evaluate $$f(x) = 3x^2$ - 2x + 1 at$$ $$x = -2.$$

Accepted Answer

$$17$$

Question 9

Given the points $$(-4, 3)$$ and $$(-8, -3)$$, what is the equation of the line in slope-intercept form?

Accepted Answer

Question 10

The Pool Fun Company sells 9000 Fun Noodles at $$2 each and 6000 at 3 $$each. Assuming a linear relationship, what is the equation relating price $$x to $$number sold $$y$$?

Accepted Answer

$$y = -3000x + 15000$$

Question 11

Which transformation is needed to graph $$g(x) = (x - 4)^2$ from the basic function f(x$$) = $$x^2$$?

Accepted Answer

Shift 4 units to the right

Question 12

Find the inverse of $$f(x) = 2x + 4$$ for $$x \leq 0.$$

Accepted Answer

$$f^{-1}(x$$) = \frac{x - 4}{2}$$

Question 13

Given $$f(x) = x^2$ + 3x$$ and $$g(x) = x + 2$$, find $$(f + g)(x)$$ and its domain.

Accepted Answer

$$(f + g)(x) = x^2$ + 4x + 2$$, Domain: $$(-\infty, \infty)$$

Question 14

Which of the following functions is even?

Accepted Answer

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

Question 15

Given $$f(x) = \frac{1}{x - 1}$$ and $$g(x) = x + 5$$, find $$(f \circ g)(x)$$ and its domain.

Accepted Answer

$$(f \circ g)(x) = \frac{1}{x + 4}$$, Domain: $$(-\infty, -4) \cup (-4, \infty)$$

Question 16

Which of the following best describes the symmetry of $$f(x) = x^3$ - 4x$$?

Accepted Answer

Odd function; symmetric about the origin

Question 17

Given the graph in image 2, what is the domain and range?

Accepted Answer

Domain: $$[-4, \infty)$$, Range: $$[-2, \infty)$$

Question 18

Given $$f(x) = \frac{1}{x + 1}$$, find the inverse function.

Accepted Answer

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

Question 19

Which of the following is the equation of the piecewise-defined function graphed in image 3?

Accepted Answer

$$f(x) = \begin{cases} -x - 4 & x \leq -3 \ 2x + 3 & x \u003e -3 \end{cases}$$

College Algebra Study Guide: Functions, Domains, Graphs, and Transformations

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