Intro to Rational Functions

A rational function must have an input variable in the denominator of a fraction.

• true

• false

Tags

CCSS.HSF-IF.C.7D

Which of the following functions is a rational function?

• $y=7-\frac{1}{x^2}$

• $y=4x^3+2x^2-3$

• $y=6\sqrt{x+3}-6$

• $y=\frac{4x}{7}+1$

Describe the transformation from the rational parent function to function f: $f\left(x\right)=\frac{1}{x+2}-1$  

• shift up 1, right 2

• shift down 1, left 2

• shift up 1, left 2

• shift down 1, right 2

Tags

CCSS.HSF.BF.B.3

Describe the transformation from the rational parent function to the function g (check all boxes that apply): $g\left(x\right)=\frac{2}{x-3}+5$  

• shift up 5

• shift right 3

• shift left 3

• vertical stretch by a factor of 2

• vertical reflection

Tags

CCSS.HSF.BF.B.3

 $f\left(x\right)=\frac{-5}{x+4}-3$  

Describe the transformation from the rational parent function to the function f (check all boxes that apply):

• shift down 3

• shift left 4

• shift right 4

• vertical stretch by a factor of 5

• vertical reflection

Tags

CCSS.HSF.BF.B.3

Describe the transformation from the rational parent function to the function f (check all boxes that apply): $f\left(x\right)=-5-\frac{4}{x+1}$  

• shift left 1

• shift right 5

• shift down 5

• vertical stretch by a factor of 4

• vertical reflection

Tags

CCSS.HSF.BF.B.3

What are the transformations?
y=(x-2)³+4

• Horz shift right 2      Vert shift up 4
• Horz shift left 2    Vert shift up 4
• Horz shift right 2      Vert shift down 4
• Horz shift left 2      Vert shift down 4

Tags

CCSS.HSF.BF.B.3

What transformations has the function undergone?

• reflect over y, vertical compression by 2, right 5, up 1
• reflect over x, vertical  compression by 2, left 5, up 1
• reflect over x, vertical stretch by 2, right 5, up 1
• reflect over y, vertical stretch by -2, right 5, up 1

Tags

CCSS.HSF.BF.B.3

Describe the transformation of the graph  y = -(x - 4)³ + 5

• Up 5 and Left 4 
• Reflect x-axis, Left 4, Up 5
• Reflect x-axis, Right 4, Up 5
• Right 4 and up 5

Tags

CCSS.HSF.BF.B.3

Which equation below is a cubic function translated left 4 units?

• y = x³ + 4
• y = (x + 4)³
• y = (x - 4)³
• y = 4x³

Tags

CCSS.HSF.BF.B.3