Q: Complete the statement using the graph of the rational function shown: As $$x \to 6^-$$, $$f(x) \to$$

As $$x \to 6^-$$, $$f(x) \to -\infty$$

Question 1

For the given solution set \{2, -1\}, write a quadratic equation in general form.

Accepted Answer

$$x^2 - 3x + 2$

Question 2

Find the solution set for the following inequality and express the answer in interval notation: $$\frac{9x + 2}{-5} \leq 3x + 2$$

Accepted Answer

$$(-\infty, -\frac{1}{2}]$$

Question 3

Determine if the following relation is a function. If so, find its domain and range: \{(1, 11), (1, 22), (3, 8), (3, 10)\}

Accepted Answer

Not a function

Question 4

Given the table of x and y-values shown, identify if it represents a function. Also, find the domain and range.

Accepted Answer

Function; Domain: \{-5, -9, -17\}; Range: \{5, 9, 17\}

Question 5

For the given conditions: Slope $$= -2$$, passing through $$(-3, -\frac{1}{3})$$, write an equation for the line in Slope-intercept form by first going through the point-slope form.

Accepted Answer

$$y = -2x - \frac{19}{3}$$

Question 6

For a circle with center $$(-8, -16)$$ and radius $$r = \sqrt{8}$$, find its equation in standard form.

Accepted Answer

$$(x + 8)^2$ + (y + 16)^2$ = 8$$

Question 7

Which graph correctly represents $$h(x) = 3\sqrt{x + 4} as a $$transformation of $$f(x) = \sqrt{x}$$?

Accepted Answer

First graph (red curve starts at $$x = -4$$, passes through $$(0, 6))$$

Question 8

Which graph correctly represents $$g(x) = -|5x + 5| + \frac{3}{2} as a $$transformation of $$f(x) = |5x|$$?

Accepted Answer

First graph (vertex at $$(-1, 1.5))$$

Question 9

Given $$f(x) = 7x - 2$$ and $$g(x) = x + 10$$, find $$fg(x)$$ and identify the domain.

Accepted Answer

$$fg(x) = 71x - 2$$; Domain: $$(-\infty, \infty)$$

Question 10

Find the equation of the parabola in vertex form for the following conditions: (a) Shape of the parabola same as $$f(x) = 13x^2$ (b) vertex at (-1$$, -1)$$.

Accepted Answer

$$y = 13(x + 1)^2$ - 1$$

Question 11

If $$1 is a $$zero of the polynomial $$f(x) = x^3$ + 13x^2$ - 14$$, solve for all the other zeros.

Accepted Answer

$$x = -7 + \sqrt{35}$$ and $$x = -7 - \sqrt{35}$$

Question 12

Determine the end behavior of the graph of the polynomial function $$f(x) = 2x^4$ + 19x^2$ - 3x - 2$$ using the Leading Coefficient Test.

Accepted Answer

Graph rises to the left and right

Question 13

Find the quotient and indicate the remainder, $$r(x)$$, if long division is performed on $$(4x^5$$ + $$2x^3$$ + $$8x^2$$) \div $$(5x^2 + 3$$)$$.

Accepted Answer

$$\frac{4x^3$}{5} + \frac{2x}{25} - \frac{8}{5} + \frac{6x/25 - 24/5}{5x^2$ + 3}$$

Question 14

The characteristics of the graph of a rational function $$f$$ are given below. Find $$f(x). x-$$intercepts: $$(0, 0)$$; vertical asymptotes: $$x = -2$$ and $$x = 2$$; horizontal asymptote: $$y = 0.$$

Accepted Answer

$$f(x) = \frac{x}{(x - 2)(x + 2)}$$

Question 15

Complete the statement using the graph of the rational function shown: As $$x 	o 6^-$$, $$f(x) 	o$$

Accepted Answer

As $$x 	o 6^-$$, $$f(x) 	o -\infty$$

College Algebra Study Guidance – Functions, Graphs, and Transformations

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