Graphs of Rational Functions

Which is the graph of $f\left(x\right)=\frac{1}{x}$ ?

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How does the graph of $g\left(x\right)=\frac{1}{x+4}$  compare to the graph of  $f\left(x\right)=\frac{1}{x}$  ?  

• It is located 4 units higher.

• It is located 4 units to the right.

• It is located 4 units to the left.

• It is 4 times taller.

Tags

CCSS.HSF.BF.B.3

How does the graph of $g\left(x\right)=\frac{1}{x}-3$  compare to the graph of  $f\left(x\right)=\frac{1}{x}$  ?  

• It is located 3 units higher.

• It is located 3 units lower.

• It is located 3 units to the left.

• It is reflected over the x-axis.

Tags

CCSS.HSF.BF.B.3

Fill in the blanks: The line x = 0 is the  _________   _________ of the graph of $f\left(x\right)=\ \frac{1}{x}$ .

• horizontal asymptote

• vertical asymptote

• y-intercept

• x-intercept

Tags

CCSS.HSF-IF.C.7D

Fill in the blanks: The line y = 0 is the  ____________  ___________ of the graph of $f\left(x\right)=\ \frac{1}{x}$ .

• horizontal asymptote

• vertical asymptote

• y-intercept

• x-intercept

Tags

CCSS.HSF-IF.C.7D

Which of these is the graph of $y=\frac{x^2+1}{x}$   ?

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Tags

CCSS.HSF-IF.C.7D

Which of these is the graph of $y=\frac{x^3+1}{x}$   ?

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Which of these is the correct graph of $y=\frac{1}{x^2}$   ?

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Which of these is the correct graph of $y=\frac{x^3}{x}$   ?

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Which of these functions will look like a cubic function "on the ends"?

•  $f\left(x\right)=\frac{1}{5x^4+3x^3-2x^2+7x+9}$  

•  $f\left(x\right)=\frac{5x^4+3x^3-2x^2+7x+9}{x^2+7}$  

•  $f\left(x\right)=\frac{5x^3+3x^2-2x+7}{x+7}$  

•  $f\left(x\right)=\frac{5x^4+3x^3-2x^2+7x+9}{x+7}$