Transformations

Given  $f\left(x-3\right)+5$  . What transformations took place from the original function f(x)?

• Left 3 and up 5

• Right 3 and down 5

• Left 3 and down 5

• Right 3 and up 5

Tags

CCSS.HSF.BF.B.3

If the blue graph is f(x) (the original function) and the red graph is the transformation, what is the equation of the red graph?

• -f(x)
• f(-x)
• f^-1(x)
• f(2x)

The blue function is the original function f(x) = x³. Which of the following is the correct equation for the red function, g(x)?

• $g\left(x\right)=x^3+1$

• $g\left(x\right)=x^3-1$

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

• $g\left(x\right)=\left(x+1\right)^3$

Identify the transformation from the graph of  $f\left(x\right)=\sin\left(x\right)$  to the graph of $g(x)=-\sin(x+5)$  

• shifted up five units

  reflection in x-axis

• shifted down five units

  reflection in x-axis

• shifted left 5 units

  reflection x-axis

• shifted right 5 units

  reflection x-axis

Tags

CCSS.HSF-IF.C.7E

 $3f\left(x-2\right)$  Identify the transformations. 

• horizontal shift to the left 2 and vertical stretch by a factor of 3

• horizontal shift to the right 2 and vertical stretch by a factor of 3

• horizontal shift to the right 2 and vertical shrink by a factor of 3

• horizontal shift to the left 2 and vertical shrink by a factor of 3

If the yellow curve has equation $f(x)=x^2$  

• Then the blue curve is  $f(x)=x^2-c$  

• Then the blue curve is  $f(x)=(x+c)^2$  

• Then the blue curve is  $f(x)=(x-c)^2$  

• Then the blue curve is  $f(x)=x2+c$  

The original function has equation $f(x)=\frac{2}{3}\sqrt{x-7}$ 

State the transformations given the new function

• Vertical Compression of ⅔
  Right 7

• Horizontal Compression of ⅔
  Left 7

• Left ⅔

  Vertical stretch of 7

• Right ⅔

  Horizontal stretch of 7

If the original function is f(x) then state the transformation that takes  $f\left(x\right)$   to $g(x)=|-x+3|$ 

• Left 3 then Reflect over y-axis

• Right 3 then Reflect over y-axis

• Left 3 then Reflect over x-axis

• Right 3 then Reflect over x-axis

 $f\left(x\right)$ is transformed so that it maps onto  $g\left(x\right)$ . Which equation would correctly represent  $g\left(x\right)$ ?

•  $g(x)=2f(x)$  

•  $g(x)=\frac{1}{2}f(x)$  

•  $g(x)=f(x)+2$  

•  $g(x)=f(x+2)$  

Describe the transformation of $y=f\left(x\right)$  to the new function  $y=f\left(\frac{1}{5}x\right)$ 

• Horizontal compression by a factor of 1/5

• Vertical stretch be a factor of 5

• Vertically compression by a factor of 1/5

•  Horizontal stretch by a factor of 5