Q: Which of the following best describes the end behavior of $$f(x) = 200x$$^{10}$$ + 4.5x^5$ - 456$$?

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

Q: Given $$f(x) = (x-1)(x-3)(x+1)^2$, what is the end behavior of f(x$$)$$?

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

Question 1

Given the function $$f(x) = x^2$ + 6x - 2$$, what are the coordinates of the vertex of the parabola?

Accepted Answer

$$(-3, -11)$$

Question 2

For the function $$f(x) = x^2$ + 6x - 2$$, what are the exact $$x-$$intercepts in simplified form?

Accepted Answer

$$x = -3 \pm \sqrt{11}$$

Question 3

Given the function $$f(x) = |x|$$, what is the equation for $$g(x)$$, which is the graph of $$f(x)$$ reflected across the $$x-$$axis and stretched horizontally by a factor of 2?

Accepted Answer

$$g(x) = -\frac{1}{2}|x|$$

Question 4

A company models its revenue $$R(x) as a $$function of the number of calculators sold, $$x$$, by $$R(x) = x \left( -\frac{1}{2}x + 100 \right). $$What number of calculators maximizes the revenue?

Accepted Answer

$$x = 100$$

Question 5

Given the rational function $$f(x) = \frac{x^2$ + 6x + 5}{2x^2$ + 7x + 5}$$, what are the equations of the vertical asymptotes?

Accepted Answer

$$x = -1, x = -\frac{5}{2}$$

Question 6

For the function $$f(x) = \sqrt{x^2$ + 5x + 2}$$, what is the domain?

Accepted Answer

$$(-\infty, -2] \cup [-1, \infty)$$

Question 7

Given $$f(x) = (x-1)(x+2)^2$, for which values of x$ is $$\frac{$$(x-1)(x+2)^2$$}{x(x-3)} \leq 0$$?

Accepted Answer

$$[-2, 0) \cup (0, 3)$$

Question 8

A polynomial $$f(x)$$ has degree 3, crosses the $$x-$$axis at $$(2,0)$$, and touches the $$x-$$axis at $$(-3,0). $$Which of the following could be its equation?

Accepted Answer

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

Question 9

Given the function $$f(x) = (x-1)(x-3)(x+1)^2$, what is the y$-intercept?

Accepted Answer

$$f(0) = -3$$

Question 10

Which transformation describes $$h(x) = 5|x-2| + 3$$ relative to $$f(x) = |x|$$?

Accepted Answer

Shifted right 2, stretched vertically by 5, shifted up 3

Question 11

Given the function $$f(x) = (x-1)(x+2)^2$, what is the multiplicity of the zero at x = -2$ and does the graph cross or touch the x$-axis at this point?

Accepted Answer

Multiplicity 2, touches the $$x-$$axis

Question 12

Which of the following best describes the end behavior of $$f(x) = 200x$$^{10}$$ + 4.5x^5$ - 456$$?

Accepted Answer

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

Question 13

Given the rational function $$f(x) = \frac{x^2$ + 6x + 5}{2x^2$ + 7x + 5}$$, what is the equation of the horizontal asymptote?

Accepted Answer

$$y = \frac{1}{2}$$

Question 14

A scatterplot of data shows a pattern that curves upward and then levels off. Which type of model is most appropriate for this data?

Accepted Answer

Neither

Question 15

If $$g(x) = -f(x+2)$$, which transformation is applied to $$f(x) to $$obtain $$g(x)$$?

Accepted Answer

Reflected across the $$x-$$axis and shifted left 2

Question 16

Given $$f(x) = (x-1)(x-3)(x+1)^2$, what is the end behavior of f(x$$)$$?

Accepted Answer

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

Question 17

For the function $$f(x) = \sqrt{x^2$ + 5x + 2}$$, which of the following intervals is NOT included in the domain?

Accepted Answer

$$(-2, -1)$$

Question 18

Given the function $$f(x) = (x-1)(x+2)^2$, what is the x$-intercept with the highest multiplicity?

Accepted Answer

$$x = -2$$

Question 19

If $$h(x) = \frac{1}{2}f(x) - 1$$, what transformation is applied to $$f(x) to $$obtain $$h(x)$$?

Accepted Answer

Compressed vertically by a factor of $$\frac{1}{2}$$ and shifted down 1

College Algebra: Functions, Graphs, Transformations, and Applications – Study Guide

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