Q: Which of the following describes the end behavior of the polynomial $$f(x) = -2x^5$ + 7x^3$ - x + 4$$?

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

Question 1

Given the parent function $$f(x) = x^2$, which of the following is the correct equation for the function that results from reflecting f(x$$)$$ over the x$-axis and then shifting it up by 3 units?

Accepted Answer

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

Question 2

Which of the following describes the end behavior of the polynomial $$f(x) = -2x^5$ + 7x^3$ - x + 4$$?

Accepted Answer

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

Question 3

Given the function $$f(x) = \dfrac{2x+1}{x-3}$$, what is the domain of $$f(x) in $$interval notation?

Accepted Answer

$$(-\infty, 3) \cup (3, \infty)$$

Question 4

Which of the following is the correct transformation of the graph of $$g(x) = \sqrt{x} to$$ $$h(x) = \sqrt{x-4} + 2$$?

Accepted Answer

Shift right 4 units and up 2 units

Question 5

A quadratic function is given in vertex form as $$f(x) = 2(x-1)^2$ - 5. $$What are the coordinates of the vertex?

Accepted Answer

$$(1, -5)$$

Question 6

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

Accepted Answer

$$7$$

Question 7

Which of the following is the correct standard form of the quadratic function $$f(x) = (x+2)(x-5)$$?

Accepted Answer

$$f(x) = x^2$ - 3x - 10$$

Question 8

If $$f(x) = 4^x$$, what is the horizontal asymptote of its graph?

Accepted Answer

$$y = 0$$

Question 9

Given the function $$f(x) = \log_2$(x-1)$$, what is the domain of $$f(x)$$?

Accepted Answer

$$(1, \infty)$$

Question 10

A polynomial $$f(x) = (x-2)^2$(x+1) is $$given. Which statement about its zeros is correct?

Accepted Answer

$$x=2 is a $$zero of multiplicity 2; $$x=-1 is a $$zero of multiplicity 1

Question 11

Which of the following best describes the transformation from $$f(x) = x^3$ to g(x$$) = $$-2(x+1)^3 + 4$?

Accepted Answer

Reflect over $$x-$$axis, stretch vertically by 2, shift left 1 unit, shift up 4 units

Question 12

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

Accepted Answer

$$x = 3$$

Question 13

Which of the following is the correct equation of a line passing through the point $$(2, 5)$$ with a slope of $$-4$$?

Accepted Answer

$$y - 5 = -4(x - 2)$$

Question 14

If $$f(x) = x^2$ - 4x + 3$$, what are the $$x-$$intercepts of the function?

Accepted Answer

$$x = 1$$ and $$x = 3$$

Question 15

Given the exponential function $$f(x) = 5e$$^{2x}$$, what is the y$-intercept?

Accepted Answer

$$5$$

Question 16

Which of the following is the correct vertex form of the quadratic $$f(x) = x^2$ + 6x + 8$$?

Accepted Answer

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

Question 17

A company models its revenue with the function $$R(x) = -2x^2$ + 12x + 5$$, where $$x is $$the number of units sold (in thousands). What is the maximum revenue, and for how many units sold does it occur?

Accepted Answer

Maximum revenue is $$R(3) = 23 at$$ $$x = 3 (3$$,000 units)

Question 18

Given the polynomial $$f(x) = x^3$ - 4x^2$ + 4x$$, use the Rational Root Theorem to determine which of the following is a possible rational zero.

Accepted Answer

$$x = 1$$

Question 19

Which of the following statements is true about the graph of $$f(x) = \dfrac{1}{x-2}$$?

Accepted Answer

It has a vertical asymptote at $$x = 2$$ and a horizontal asymptote at $$y = 0$$

Question 20

Given the function $$f(x) = 3(x-2)^2$ + 1$$, which of the following describes the sequence of transformations from the parent function $$g(x) = x^2$?

Accepted Answer

Shift right 2 units, stretch vertically by 3, shift up 1 unit

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

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