a. Find the slant asymptote of the graph of the rational function.
b. Follow the seven-step strategy and use the slant asymptote to graph the rational function.
$f (x) = \frac{x^{2} + 2 x - 8}{x - 4}$
a. Select the correct choice below and, it necessary, till in the answer box to complete the choice.
A. The equation of the slant asymptote is $y = x + 6$
(Type an equation.)
B. There is no slant asymptote.
b. To graph the function, first determine the symmetry of the graph of $f$ . Choose the correct answer below.
origin symmetry
neither $y$ -axis symmetry nor origin symmetry
y-axis symmetry

What is the $y$ -intercept? Select the correct choice below and, if necessary, fill in the answer box to complete the choice.
A. The $y$ -intercept is
(Type an integer or a simplified fraction.)
B. There is no $y$ -intercept.

Answer

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Final Answer: The equation of the slant asymptote is $y = x$ and the y-intercept is $2$ .

Steps

Step 1 ：The question is asking for the slant asymptote of the given rational function. A slant asymptote occurs when the degree of the numerator is one more than the degree of the denominator. In this case, the degree of the numerator is 2 and the degree of the denominator is 1, so there is a slant asymptote.

Step 2 ：To find the slant asymptote, we can perform polynomial division. The quotient of the division will be the equation of the slant asymptote.

Step 3 ：After finding the slant asymptote, we can find the y-intercept of the function by setting x to 0 in the function.

Step 4 ：The slant asymptote of the function is $y = x$ and the y-intercept is 2.

Step 5 ：Final Answer: The equation of the slant asymptote is $y = x$ and the y-intercept is $2$ .

Answer

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