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

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

Question 1

Given the parent function $$f(x) = x^2$, which transformation results in the function g(x) = (x$$ - $$3)^2 + 5$?

Accepted Answer

A horizontal shift 3 units right and a vertical shift 5 units up

Question 2

Which of the following is the domain of the function $$f(x) = \dfrac{1}{x^2$ - 4}$$?

Accepted Answer

$$x 
eq 2$$ and $$x 
eq -2$$

Question 3

Given the quadratic function $$f(x) = 2(x - 1)^2$ - 3$$, what is the vertex of the graph?

Accepted Answer

$$(1, -3)$$

Question 4

If the equation of a line is $$y = -3x + 7$$, what is the slope and y-intercept?

Accepted Answer

Slope: $$-3$$, y-intercept: $$7$$

Question 5

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

Accepted Answer

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

Question 6

Given the exponential function $$f(x) = 3 \cdot 2$$^{x-4}$$, what is the horizontal asymptote?

Accepted Answer

$$y = 0$$

Question 7

Which of the following is the correct interval notation for the domain of $$f(x) = \sqrt{x + 5}$$?

Accepted Answer

$$[-5, \infty)$$

Question 8

A company models its profit with the function $$P(x) = -x^2$ + 6x - 8$$, where $$x is $$the number of units sold. What is the maximum profit, and how many units must be sold to achieve it?

Accepted Answer

Maximum profit is $$1 at$$ $$x = 3$$

Question 9

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

Accepted Answer

$$x = 3$$ and $$x = -3 ($$excluding $$x = -3$$ due to domain restriction)

Question 10

Which transformation is applied to the parent function $$f(x) = \log(x) to $$obtain $$g(x) = \log(x - 2) + 4$$?

Accepted Answer

Shift 2 units right and 4 units up

Question 11

Given the quadratic function $$f(x) = x^2$ - 6x + 8$$, what are its zeros?

Accepted Answer

$$x = 2$$ and $$x = 4$$

Question 12

Which of the following is the equation of a line passing through $$(2, 5)$$ with a slope of $$-3$$?

Accepted Answer

$$y = -3x + 11$$

Question 13

If $$f(x) = x^2$ and g(x) = f(x + 2) - 5$, what is the vertex of g(x$$)$$?

Accepted Answer

$$(-2, -5)$$

Question 14

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

Accepted Answer

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

Question 15

Given the polynomial $$f(x) = x^3$ - 4x^2$ + 5x - 2$$, which of the following is a possible rational root according to the Rational Root Theorem?

Accepted Answer

$$x = 2$$

Question 16

Which of the following is the equation of a quadratic function with vertex $$(3, -2)$$ and opening upward?

Accepted Answer

$$y = (x - 3)^2$ - 2$$

Question 17

Given the function $$f(x) = \dfrac{2x}{x^2$ - 1}$$, what is the domain?

Accepted Answer

$$x 
eq 1$$ and $$x 
eq -1$$

Question 18

Which of the following is the correct transformation sequence to graph $$f(x) = -2(x + 1)^2$ + 3$$ from the parent function $$f(x) = x^2$?

Accepted Answer

Shift left 1, reflect over x-axis, stretch vertically by 2, shift up 3

Question 19

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

Accepted Answer

$$x \u003e 1$$

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

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