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 $$x \to -\infty$$, $$f(x) \to \infty$$

Q: Which of the following is the parent function for all exponential functions?

$$f(x) = a^x$$, where $$a \u003e 0$$ and $$a \neq 1$$

Question 1

Given the parent function $$f(x) = x^2$, which of the following is the correct equation for a graph that is reflected over the x-axis, shifted 3 units to the right, and 2 units up?

Accepted Answer

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

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

What is the domain of the function $$f(x) = \dfrac{2x+1}{x^2$-9} in $$interval notation?

Accepted Answer

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

Question 4

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

Accepted Answer

$$(1, -5)$$

Question 5

A company models its revenue with the function $$R(x) = -5x^2$ + 200x$$, where $$x is $$the number of units sold. What is the maximum revenue, and how many units must be sold to achieve it?

Accepted Answer

Maximum revenue is $$2000 at$$ $$x = 20$$ units

Question 6

Which of the following is the correct transformation of the parent exponential function $$f(x) = 2^x to$$ $$g(x) = 2$$^{x-3}$$ + 4$$?

Accepted Answer

Shift right 3 units and up 4 units

Question 7

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

Accepted Answer

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

Question 8

What is the axis of symmetry for the quadratic function $$f(x) = 4(x+2)^2$ - 9$$?

Accepted Answer

$$x = -2$$

Question 9

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

Accepted Answer

$$(1, \infty)$$

Question 10

Given the polynomial $$f(x) = (x-2)^2$(x+1)$$, what is the multiplicity of the zero at $$x = 2$$ and what does the graph do at this zero?

Accepted Answer

Multiplicity 2; the graph touches and turns at $$x = 2$$

Question 11

Which of the following is the correct standard form of the quadratic function with vertex at $$(3, -4)$$ and passing through the point $$(5, 0)$$?

Accepted Answer

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

Question 12

Given $$f(x) = x^3$ - 4x^2$ + 5x - 2$$, use the Rational Root Theorem to determine which of the following is a possible rational zero.

Accepted Answer

$$x = 2$$

Question 13

Which of the following statements is true about the horizontal asymptote of the function $$f(x) = \dfrac{3x^2$ + 1}{x^2$ - 4}$$?

Accepted Answer

$$y = 3$$

Question 14

A population of bacteria is modeled by $$P(t) = 500 \cdot 2$$^{t}$$, where t$ is in hours. How many bacteria will there be after 5 hours?

Accepted Answer

$$16,000$$

Question 15

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

Accepted Answer

$$x = 2$$

Question 16

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

Accepted Answer

$$y = -3x + 11$$

Question 17

If $$f(x) = (x+1)(x-4)$$, what are the x-intercepts of the graph?

Accepted Answer

$$x = -1$$ and $$x = 4$$

Question 18

Given the quadratic function $$f(x) = x^2$ - 6x + 8$$, convert it to vertex form.

Accepted Answer

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

Question 19

Which of the following is the parent function for all exponential functions?

Accepted Answer

$$f(x) = a^x$$, where $$a \u003e 0$$ and $$a 
eq 1$$

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

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