Q: Which of the following describes the end behavior of 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: Given $$f(x) = \frac{x^2$ - 9}{x + 3}$$, what is the simplified form and what is the domain?

$$f(x) = x - 3$$, domain: $$x \neq -3$$

Q: Given $$f(x) = \frac{1}{x^2$}$$, what is the end behavior of the function?

As $$x \to \infty$$, $$f(x) \to 0$$; as $$x \to -\infty$$, $$f(x) \to 0$$

Question 1

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

Accepted Answer

A shift 3 units right and 2 units up

Question 2

What is the domain of the function $$f(x) = \sqrt{x-5}$$?

Accepted Answer

$$x \geq 5$$

Question 3

Given the quadratic function $$f(x) = -2(x+1)^2$ + 4$$, what is the vertex of the graph?

Accepted Answer

$$(-1, 4)$$

Question 4

Which of the following describes the end behavior of 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

A company models its revenue with $$R(x) = 50x - x^2$, where x$ is the number of units sold. What is the maximum revenue, and how many units should be sold to achieve it?

Accepted Answer

Maximum revenue is $$625 at$$ $$x = 25$$

Question 6

Given the function $$f(x) = \frac{2x+1}{x-4}$$, what is the vertical asymptote?

Accepted Answer

$$x = 4$$

Question 7

Which of the following is the axis of symmetry for the quadratic function $$f(x) = x^2$ - 6x + 5$$?

Accepted Answer

$$x = 3$$

Question 8

If $$f(x) = 2^x$$, what is the horizontal asymptote of its graph?

Accepted Answer

$$y = 0$$

Question 9

A quadratic function in vertex form is $$f(x) = 3(x-2)^2$ + 5. $$Convert it to standard form.

Accepted Answer

$$f(x) = 3x^2$ - 12x + 17$$

Question 10

Given the polynomial $$f(x) = (x-2)^2$(x+1)$$, what are the zeros and their multiplicities?

Accepted Answer

$$x = 2 ($$multiplicity 2), $$x = -1 ($$multiplicity 1)

Question 11

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

Accepted Answer

$$y = -3x + 11$$

Question 12

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

Accepted Answer

$$x \u003e 1$$

Question 13

Which transformation is applied to $$f(x) = x^3$ to obtain g(x$$) = $$-x^3 + 4$?

Accepted Answer

Reflection over the $$x-$$axis and shift up 4 units

Question 14

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

Accepted Answer

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

Question 15

A population of bacteria grows according to $$P(t) = 500e$$^{0.2t}$$. What is the initial population?

Accepted Answer

$$500$$

Question 16

Given $$f(x) = \frac{x^2$ - 9}{x + 3}$$, what is the simplified form and what is the domain?

Accepted Answer

$$f(x) = x - 3$$, domain: $$x 
eq -3$$

Question 17

Which of the following is the correct factored form of $$f(x) = x^3$ - 8$$?

Accepted Answer

$$(x-2)(x^2 + 2x + 4$$)$$

Question 18

If $$f(x) = 4x^2$ - 12x + 9$$, what is the vertex of the parabola?

Accepted Answer

$$(1.5, 0)$$

Question 19

Given $$f(x) = \frac{1}{x^2$}$$, what is the end behavior of the function?

Accepted Answer

As $$x 	o \infty$$, $$f(x) 	o 0$$; as $$x 	o -\infty$$, $$f(x) 	o 0$$

Question 20

A quadratic function $$f(x)$$ opens downward and has its vertex at $$(2, 7). $$Which could be its equation?

Accepted Answer

$$f(x) = -a(x-2)^2$ + 7$$, where $$a \u003e 0$$

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

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