Math  /  Algebra

QuestionFollow the steps for graphing a rational function to graph the function R(x)=x2+10x+16x+8R(x)=\frac{x^{2}+10 x+16}{x+8}. (Type integers or simplified fractions. Use a comma to separate answers as needed. Type each answer only once.) C. The graph has neither xx-intercepts nor yy-intercepts. D. The graph has xx-intercept(s) \square and no yy-intercept(s). (Type integers or simplified fractions. Use a comma to separate answers as needed. Type each answer only once.) Determine the behavior of the graph of RR at any xx-intercepts. Select the correct choice and, if necessary, fill in the answer box(es) within your choice. A. The graph will cross the xx-axis at x=x= \square and touch the xx-axis at x=x= \square (Type integers or simplified fractions. Use a comma to separate answers as needed. Type each answer only once.) B. The graph will cross the xx-axis at x=2x=-2. \square (Type an integer or a simplified fraction. Use a comma to separate answers as needed. Type each answer only once.) C. The graph will touch the xx-axis at x=x= \square (Type an integer or a simplified fraction. Use a comma to separate answers as needed. Type each answer only once.) D. There is no x-intercept.
Determine the vertical asymptote(s), if any exist. Select the correct choice and, if necessary, fill in the answer box(es) within your choice. A. The function has one vertical asymptote, \square . (Type an equation. Use integers or fractions for any numbers in the equation.) B. The function has two vertical asymptotes. The leftmost asymptote is \square , and the rightmost asymptote is \square (Type equations. Use integers or fractions for any numbers in the equations.) C. The function has three vertical asymptotes. The leftmost asymptote is \square , the middle asymptote is \square , and the rightmost asymptote is \square . (Type equations. Use integers or fractions for any numbers in the equations.) D. The function has no vertical asymptote.
Determine the hole, if it exists. Select the correct choice and, if necessary, fill in the answer box to complete your choice.
There is a hole in the graph at the point \square \square. (Type an ordered pair using integers or fractions.) B. There are no holes in the graph.

Studdy Solution
D. The graph has x-intercept(s) 2-2 and no y-intercept(s). B. The graph will cross the x-axis at x=2x=-2. D. The function has no vertical asymptote. There is a hole in the graph at the point (8,6)(-8, -6).

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