IndividualTransformations 9.17.20

Describe the transformation of

 $f\left(x\right)=x^2$  if we apply  $g\left(x\right)=-f\left(x+8\right)-15$  

• The graph will reflect over the x-axis, shift 8 units right and shift 15 units down.

• The graph will reflect over the x-axis, shift 8 units left and shift 15 units down.

• The graph will reflect over the y-axis, shift 8 units right and shift 15 units up.

Describe the transformation of  $f\left(x\right)=x^2$  if we apply  $g\left(x\right)=f(x-12)-7$  

• The graph will shift 12 units to the right and 7 units down.

• The graph will shift 12 units to the left and 7 units down.

• The graph will shift 12 units to the right and 7 units up.

Describe the transformation of  $f\left(x\right)=\left|x\right|$  if we apply  $g\left(x\right)=-f\left(x+3\right)+6$  

• The graph will reflect over the x-axis, shift 3 units left and shift 6 units up.

• The graph will reflect over the x-axis, shift 3 units right and shift 6 units up.
  

• The graph will reflect over the y-axis, shift 3 units right and shift 6 units up.

Describe the transformation of  $f\left(x\right)=\left|x\right|$  if we apply  $g\left(x\right)=f\left(x-14\right)-1$  

• The graph will translate 14 units right and shift 1 unit down.

• The graph will translate 14 units right and shift 1 unit up.

• The graph will translate 14 units left and shift 1 unit down.

What is the equation of the graph?

• $f\left(x\right)=-\left(x-3\right)^2+2$

• $f\left(x\right)=\left(x-3\right)^2+2$

• $f\left(x\right)=-\left(x+3\right)^2+2$

If we apply the transformation  $-g\left(x+1\right)-2$  to the grpah what is the new function?

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

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

•  $g\left(x\right)=-\left(x+1\right)^2-1$  

If we apply the transformation  $g\left(x-2\right)+4$  to the graph, then what is the new function?

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

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

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

If we apply the transformation

 $-g\left(x+5\right)-1$  to the graph, then what is the new function?

•  $g\left(x\right)=\left(x+2\right)^2+1$  
  

•  $g\left(x\right)=\left(x+2\right)^2-1$  
  

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

Which of the following equations represents the transformation on the cubic function. Vertical stretch of 5, 12 units to the left and 1 unit down.

• f(x)= - 5(x+12)³-1

• f(x)= 5(x+12)³-1

• f(x)= - 5(x-12)³-1

• f(x)= - (x+12)³-1

The graph shows the function f(x)=x³ in blue and another function g(x) in red.  Which could be the equation for g(x)?

• A.  g(x) = -x³
• B.  g(x) = x³ - 1
• C.  g(x) = (x + 1)³
• D.  g(x) = (x - 1)³