Transformations of Parent Graphs

 If the blue graph is the parent function, what is the equation of the red (transformed) function?

• g(x)=x³+1
• g(x)=x³-1
• g(x)=(x-1)³
• g(x)=(x+1)³

Tags

CCSS.HSF.BF.B.3

Which equation shows a function that is translated left 4 and 7 up?

• y = |x + 4| + 7
• y = (x - 4)² + 7
• y = (x + 7)² - 4
• y = |x + 4| - 7

Tags

CCSS.HSF.BF.B.3

CCSS.HSG.CO.A.2

The graph shows the function f(x)=x² in blue and another function g(x) in red.  Which could be the equation for g(x)?

• A.  g(x)=3x²
• B.  g(x)=1/3x²
• C.  g(x) = x² - 3
• D.  g(x) = (x-3)²

Tags

CCSS.HSF.BF.B.3

CCSS.HSA.CED.A.2

CCSS.HSA.REI.D.11

The graph shows the function f(x)=x² in blue and another function g(x) in red. Which description could describe this transformation?

• Vertical compression by 1/2

• Horizontal compression by 1/2

• Horizontal stretch by 2

• Vertical stretch by 1/2

The parent is in purple and transformed is in black. Which equation would result in the black?

• f(x) = |2x|

• f(x)=|x|+2

• f(x)=|x|+1/2

• f(x)=|1/2x|

Tags

CCSS.HSF.BF.B.3

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

• Reflection over y-axis; Right 3; Up 1
• Right 3; Up 1
• Reflection over x-axis; Left 3; Up 1
• Reflection of x-axis; Right 3; Up 1

Tags

CCSS.HSG.CO.A.2

CCSS.HSG.CO.A.4

CCSS.HSG.CO.A.5

CCSS.HSG.CO.B.6

Which function is described by the graph shown?

(assume no stretches or compressions)

• $y=-\left(x-1\right)^3-2$
  

• $y=\left(x-1\right)^3-2$
  

• $y=-\left(-\left(x-1\right)\right)^3-2$
  

• $y=-\left(x+1\right)^3-2$
  

Which function is described by the graph shown?

(assume no stretches or compressions)

• $y=\frac{1}{x+3}-1$
  

• $y=\frac{1}{x-3}-1$
  

• $y=-\frac{1}{x+3}-1$
  

• $y=-\frac{1}{x-3}-1$
  

Tags

CCSS.HSF-IF.C.7D

 $y=\left(4x+4\right)^2-3$ 

• A vertical stretch by a factor of 4 and shift down 3; Horizontal shift left 1

• A vertical compression by a factor of 1/4 and shift down 3; horizontal shift left 4

• A horizontal stretch by a factor of 1/4 and shift right 1; vertical shift down 3
  

• A horizontal compression by a factor of 1/4 and shift left 1; vertical shift down 3

f(x) = |-x + 3|

Describe the horizontal transformations

• Reflect over y-axis

  Left 3

• Reflect over y-axis

  Right 3

• Reflect over x-axis

  Left 3

• Reflect over x-axis

  Right 3