Question 1

Solve the equation $$5x-2=7. $$What is the value of $$x$$?

Accepted Answer

Question 2

Solve the inequality $$3x-2+4 \geq 20$$ and express the solution in interval notation.

Accepted Answer

$$(6, \infty)$$

Question 3

What is the domain of the function $$f(x) = x + 3$$?

Accepted Answer

$$(-\infty, \infty)$$

Question 4

Given the function $$f(x) = x^2$ + 3x$$, find and simplify the difference quotient $$\frac{f(x+h)-f(x)}{h}$$ for $$h 
eq 0.$$

Accepted Answer

$$2x + 3 + h$$

Question 5

Which of the following best describes the transformation from the basic function $$f(x) = x^3$ to y$$ = $$(x+3)^3 - 2$?

Accepted Answer

Shift the graph 3 units to the left and 2 units down

Question 6

Given the function $$f(x) = x^3$ - 4x$$, determine whether the function is even, odd, or neither. Also, state the symmetry of its graph.

Accepted Answer

Odd; origin symmetry

Question 7

A company finds that pricing a product at $$2$$ yields $$9000$$ sales per day, and at $$3$$ yields $$6000$$ sales per day. Assuming a linear relationship, what is the equation relating price $$x to $$sales $$y$$?

Accepted Answer

$$y = -3000x + 15000$$

Question 8

Given the function $$f(x) = 3x^2$ - 2x + 1$$, evaluate $$f(-2).$$

Accepted Answer

$$17$$

Question 9

Find the inverse of the function $$f(x) = 2x + 1.$$

Accepted Answer

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

Question 10

Given the graph in Image 1, what is the domain of the function?

Accepted Answer

$$[-4, \infty)$$

Question 11

Given the graph in Image 1, for which value of $$x$$ does $$f(x) = -1$$?

Accepted Answer

$$x = -2$$

Question 12

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

Accepted Answer

$$(-\infty, \infty)$$

Question 13

Which of the following is the correct simplified form of $$f(a+3)$$ for $$f(x) = 3x^2$ - 2x + 1$$?

Accepted Answer

$$3a^2 + 16a + 22$

Question 14

Given $$f(x) = x^4$ + 2$$ for $$x \leq 0$$, what is the inverse function $$f^{-1}(x$$)$$?

Accepted Answer

$$f^{-1}(x$$) = -\sqrt[4]{x-2}$$

Question 15

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

Accepted Answer

Shift the graph 4 units to the right and 2 units down

Question 16

Given $$f(x) = 1 + 5x$$ and $$g(x) = x - 1$$, what is the domain of $$(f+g)(x)$$?

Accepted Answer

$$[1, \infty)$$

Question 17

Given $$f(x) = 1 + 5x$$ and $$g(x) = x - 1$$, what is $$(f \circ g)(x)$$?

Accepted Answer

$$1 + 5(x - 1)$$

Question 18

Given the graph in Image 5, which function does it most likely represent?

Accepted Answer

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

Question 19

Given $$f(x) = 2x^2$ - 3x - 4$$, find and simplify the difference quotient $$\frac{f(x+h)-f(x)}{h}$$ for $$h 
eq 0.$$

Accepted Answer

$$4x - 3 + 2h$$

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

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