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

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 $$f(x) = 3x^4$ - 2x^2$ + 7$$?

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

Question 1

Given the parent function $$f(x) = x^2$, which of the following is the correct graph of g(x$$) = $$-2(x-3)^2 + 5$?

Accepted Answer

A parabola opening downwards, vertically stretched by 2, shifted right 3 units and up 5 units.

Question 2

Which of the following describes the sequence of transformations from $$f(x) = \sqrt{x} to$$ $$g(x) = 3\sqrt{x+4} - 2$$?

Accepted Answer

Shift left 4 units, stretch vertically by 3, shift down 2 units.

Question 3

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

Accepted Answer

$$(-\infty, 2) \cup (2, \infty)$$

Question 4

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

Accepted Answer

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

Question 5

A company models its profit with the function $$P(x) = -2x^2$ + 8x + 10$$, 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 $$18 at$$ $$x = 4$$ units.

Question 6

Given the quadratic function $$f(x) = 2(x-1)^2$ - 5$$, what are the coordinates of the vertex?

Accepted Answer

$$(1, -5)$$

Question 7

Which of the following is the correct equation of a line with slope $$m = -\dfrac{3}{2}$$ passing through the point $$(4, 1)$$?

Accepted Answer

$$y - 1 = -\dfrac{3}{2}(x - 4)$$

Question 8

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

Accepted Answer

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

Question 9

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

Accepted Answer

$$y = 0$$

Question 10

Which of the following is the correct factored form of $$f(x) = x^3$ - 4x^2$ + 3x$$?

Accepted Answer

$$x(x-1)(x-3)$$

Question 11

A quadratic function has its vertex at $$(2, -7)$$ and passes through the point $$(4, 1). $$Which of the following is its equation in vertex form?

Accepted Answer

$$y = 2(x-2)^2$ - 7$$

Question 12

Given the rational function $$f(x) = \dfrac{x+1}{x^2$-9}$$, what are the vertical asymptotes?

Accepted Answer

$$x = 3$$ and $$x = -3$$

Question 13

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

Accepted Answer

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

Question 14

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

Accepted Answer

$$(1, \infty)$$

Question 15

If $$f(x) = (x-2)^2$ - 9$$, what are the $$x-$$intercepts?

Accepted Answer

$$x = 5$$ and $$x = -1$$

Question 16

A population of bacteria triples every hour. If the initial population is 200, which function models the population after $$t$$ hours?

Accepted Answer

$$P(t) = 200 \cdot 3^t$$

Question 17

Given the polynomial $$f(x) = x^3$ - 2x^2$ - 5x + 6$$, which of the following is a zero of the function?

Accepted Answer

$$x = 3$$

Question 18

Which of the following is the correct standard form of the quadratic function with vertex $$(1, -4)$$ and passing through $$(3, 0)$$?

Accepted Answer

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

Question 19

Given $$f(x) = \dfrac{2x+1}{x-4}$$, what is the $$y-$$intercept of the function?

Accepted Answer

$$(0, -\dfrac{1}{4})$$

College Algebra Study Guide: Transformations, Equations, and Graphs

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