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

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

Question 1

Given the parent function $$f(x) = x^2$, which of the following equations represents a reflection over the x-axis followed by a vertical shift up by 3 units?

Accepted Answer

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

Question 2

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

Accepted Answer

$$(-\infty, 4) \cup (4, \infty)$$

Question 3

A quadratic function has its vertex at $$(2, -5)$$ and opens upward. Which of the following could be its equation?

Accepted Answer

$$f(x) = (x-2)^2$ - 5$$

Question 4

Given the function $$f(x) = 2x^3$ - 5x^2$ + 3x - 7$$, what is the end behavior of $$f(x) as$$ $$x 	o \infty$$?

Accepted Answer

$$f(x) 	o \infty$$

Question 5

Which of the following is the $$y-$$intercept of the function $$f(x) = 4x^2$ - 7x + 2$$?

Accepted Answer

$$(0, 2)$$

Question 6

A company models its revenue with the function $$R(x) = -2x^2$ + 8x + 10$$, 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 $$18 at$$ $$x = 2$$ thousand units

Question 7

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

Accepted Answer

$$y = 0$$

Question 8

Which of the following is the correct transformation to obtain the graph of $$g(x) = \log_{2}(x-4) + 1$$ from the parent function $$f(x) = \log$$_{2}$$x$$?

Accepted Answer

Shift right 4 units and up 1 unit

Question 9

What is the axis of symmetry for the quadratic function $$f(x) = 3(x+2)^2$ - 7$$?

Accepted Answer

$$x = -2$$

Question 10

Given the polynomial $$f(x) = (x-1)^2$(x+3)$$, which of the following statements is true about its zeros?

Accepted Answer

$$x = 1 is a $$zero of multiplicity 2; $$x = -3 is a $$zero of multiplicity 1$

Question 11

If $$f(x) = 2x + 5$$, what is the $$x-$$intercept of the function?

Accepted Answer

$$(-2.5, 0)$$

Question 12

A quadratic function in standard form is $$f(x) = -x^2$ + 6x - 8. $$What is the vertex of the parabola?

Accepted Answer

$$(3, 1)$$

Question 13

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

Accepted Answer

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

Question 14

Given the function $$f(x) = \dfrac{3x}{x^2$ - 9}$$, what are the $$x-$$intercepts?

Accepted Answer

$$(0, 0)$$

Question 15

Which of the following best describes 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 16

A population of bacteria is modeled by $$P(t) = 200 \cdot 1.05^t$$, where $$t is in $$hours. What is the initial population?

Accepted Answer

$$200$$

Question 17

Given the function $$f(x) = \dfrac{x^2$ - 9}{x - 3}$$, what is the simplified form for $$x 
eq 3$$?

Accepted Answer

$$f(x) = x + 3$$

Question 18

Which of the following is the equation of a line with slope $$-\dfrac{3}{2}$$ and $$y-$$intercept $$4$$?

Accepted Answer

$$y = -\dfrac{3}{2}x + 4$$

Question 19

If $$f(x) = (x-2)^2$ + 1$$, what is the minimum value of the function and where does it occur?

Accepted Answer

Minimum value is $$1 at$$ $$x = 2$$

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

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