Practice Rational Transformations and Characteristics

The graph below is a transformation of the parent function f(x) = 1/x. Write the equation of the graph.

• g(x) = 1/(x+3) - 4
• g(x) = 1/(x-) + 4
• g(x) = 1/(x+3) + 4
• g(x) = 1/(x-3) - 4

Identify the horizontal and the vertical asymptotes of the function shown in the graph.

• horizontal asymptote: y = -3; vertical asymptote: x = -4
• horizontal asymptote: x = 3; vertical asymptote: y = -4
• horizontal asymptote: y = -3; vertical asymptote: x = 4
• horizontal asymptote: x = -3; vertical asymptote: y = 4

Which of the following represent the graph?

• 
• 
• 
• 

What is the horizontal asymptote? 

• x = 2
• x = 7
• y = 2
• y = 7

What is the horizontal asymptote? 

• x = 2
• y = 2
• x = 1
• y = 1

What are the asymptotes?

• x=-3, y=1
• x=3, y =1
• x=-3, y =-1
• x=3 y=-1

What is the parent function of a rational function?

• Y=X²
• Y=X
• 1 / X
• Y=X / 1

How is this function transformed from the parent function?

• Translated left and up
• Translated right and up
• Translated left and down
• Translated right and down

Describe all transformations from the parent function g(x)=1/x to f(x).

• Shift right 5 and shift up 7
• Shift left 7 and shift up 5
• Reflect over the x-axis, shift up 7
• Shift left 5 and shift up 7

Describe the all the transformations to f(x) = - ¹/x - 7

• reflection and down 7

• reflection and up 7

• down 7

• left 7