Graphing rational functions

in CIPD HR Experts UK/by CIPD HELP

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Which of the following functions is graphed below?

a. $y equals fraction numerator minus 5 x squared over denominator x squared plus 9 end fraction$

b. $y equals fraction numerator 5 x squared over denominator x squared minus 9 end fraction$

c. $y equals fraction numerator 5 x squared over denominator x squared plus 9 end fraction$

d. $y equals fraction numerator minus 5 x squared over denominator x squared minus 9 end fraction$

What is the horizontal asymptote of the graph of the following function?

$y = \frac{10 x^{2} - 1}{x^{3} + 8}$

b. $y equals fraction numerator x squared plus 4 x minus 5 over denominator x minus 6 end fraction$

c. $y equals fraction numerator 2 x squared plus x over denominator x squared plus 1 end fraction$

d. $y equals fraction numerator 2 x minus 8 over denominator 3 x squared minus 9 end fraction$

Identify the equations of the vertical asymptotes of the following function.

$f (x) = \frac{3}{x^{2} - 7 x + 10}$

Which of the following functions is shown in the graph below?

a. $f left parenthesis x right parenthesis space equals space fraction numerator 3 x over denominator x squared minus 3 x space minus space 4 end fraction$

b. $f left parenthesis x right parenthesis space equals space fraction numerator 3 x over denominator x squared plus 3 x minus 4 end fraction$

c. $f left parenthesis x right parenthesis space equals space fraction numerator 3 x over denominator x squared plus 5 x plus 4 end fraction$

d. $f left parenthesis x right parenthesis space equals space fraction numerator 3 x over denominator x squared minus 5 x plus 4 end fraction$

Which of the following functions is shown in the graph below?

a. $f left parenthesis x right parenthesis space equals space fraction numerator 1 over denominator x squared plus 4 x plus 4 end fraction$

b. $f left parenthesis x right parenthesis space equals space fraction numerator 1 over denominator x squared minus 4 x plus 4 end fraction$

c. $f left parenthesis x right parenthesis space equals space fraction numerator 1 over denominator x squared plus 4 end fraction$

d. $f left parenthesis x right parenthesis space equals space fraction numerator 1 over denominator x squared minus 4 end fraction$

Which of the following functions is shown in the graph below?

a. $f left parenthesis x right parenthesis space equals space fraction numerator x cubed over denominator x squared minus 3 x space minus 4 end fraction$

b. $f left parenthesis x right parenthesis space equals space fraction numerator x squared over denominator x squared minus 3 x minus 4 end fraction$

c. $f left parenthesis x right parenthesis space equals space fraction numerator 2 x over denominator x squared minus 3 x minus 4 end fraction$

d. $f left parenthesis x right parenthesis space equals space fraction numerator x over denominator x squared minus 3 x minus 4 end fraction$

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