Q: Which of the following is the correct end behavior for the polynomial $$f(x) = -3x^5$ + 2x^3$ - x$$?

As $$x \to \infty$$, $$f(x) \to -\infty$$; as $$x \to -\infty$$, $$f(x) \to \infty$$

Q: Which of the following describes the end behavior of $$f(x) = 4x^4$ - 2x^2$ + 1$$?

As $$x \to \infty$$, $$f(x) \to \infty$$; as $$x \to -\infty$$, $$f(x) \to \infty$$

Question 1

Given the parent function $$f(x) = x^2$, which transformation results in the graph g(x) = (x$$ - $$3)^2 + 2$?

Accepted Answer

A shift 3 units right and 2 units up

Question 2

What is the domain of the function $$f(x) = \dfrac{1}{x-4}$$?

Accepted Answer

$$x 
eq 4$$

Question 3

Given the quadratic function $$f(x) = 2x^2$ - 8x + 6$$, what is the axis of symmetry?

Accepted Answer

$$x = 2$$

Question 4

Which of the following is the correct end behavior for the polynomial $$f(x) = -3x^5$ + 2x^3$ - x$$?

Accepted Answer

As $$x 	o \infty$$, $$f(x) 	o -\infty$$; as $$x 	o -\infty$$, $$f(x) 	o \infty$$

Question 5

If $$f(x) = \log_2$(x-1)$$, what is the vertical asymptote of the graph?

Accepted Answer

$$x = 1$$

Question 6

Given the exponential function $$f(x) = 5 \cdot 2$$^{x-3}$$, what is the horizontal asymptote?

Accepted Answer

$$y = 0$$

Question 7

Which of the following is the correct factored form of $$f(x) = x^2$ - 5x + 6$$?

Accepted Answer

$$(x - 2)(x - 3)$$

Question 8

A company models its revenue with $$R(x) = -2x^2$ + 40x$$, where $$x is $$the number of units sold. What is the maximum revenue, and at how many units sold does it occur?

Accepted Answer

Maximum revenue is $$800 at$$ $$x = 20$$

Question 9

Given $$f(x) = x^3$ - 4x^2$ + 4x$$, which of the following is NOT a zero of the function?

Accepted Answer

$$x = 4$$

Question 10

Which transformation is applied to the parent function $$f(x) = \sqrt{x} to $$obtain $$g(x) = -\sqrt{x+5}$$?

Accepted Answer

Reflection over the $$x-$$axis and shift 5 units left

Question 11

Given the linear equation $$y = -3x + 7$$, what is the $$y-$$intercept?

Accepted Answer

$$7$$

Question 12

Which of the following is the correct vertex form of the quadratic $$f(x) = x^2$ + 6x + 5$$?

Accepted Answer

$$f(x) = (x + 3)^2$ - 4$$

Question 13

A population of bacteria is modeled by $$P(t) = 1000e$$^{0.2t}$$, where t$ is time in hours. What is the initial population?

Accepted Answer

$$1000$$

Question 14

Given the function $$f(x) = \dfrac{x^2$ - 9}{x - 3}$$, what is the domain?

Accepted Answer

$$x 
eq 3$$

Question 15

Which of the following describes the end behavior of $$f(x) = 4x^4$ - 2x^2$ + 1$$?

Accepted Answer

As $$x 	o \infty$$, $$f(x) 	o \infty$$; as $$x 	o -\infty$$, $$f(x) 	o \infty$$

Question 16

If $$f(x) = (x - 2)^2$(x + 1)$$, what is the multiplicity of the zero at $$x = 2$$?

Accepted Answer

2

Question 17

Which parent function is used for the logarithmic function $$f(x) = \log_3$(x)$$?

Accepted Answer

$$f(x) = \log_3$(x)$$

Question 18

Given $$f(x) = x^2$ - 4$$, which of the following points is an $$x-$$intercept?

Accepted Answer

$$(2, 0)$$

Question 19

Which of the following is the correct standard form of the quadratic function with vertex form $$f(x) = 2(x - 1)^2$ + 3$$?

Accepted Answer

$$f(x) = 2x^2$ - 4x + 5$$

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

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