Transformations of Functions

If the blue function is $f\left(x\right)=x^2$ , then the red function must be

•  $g\left(x\right)=x^2-5$  

•  $g\left(x\right)=x^2+5$ 

•  $g\left(x\right)=\left(x-5\right)^2$  

•  $g\left(x\right)=\left(x+5\right)^2$  

Describe the transformation of  $y=f\left(x\right)$ for the new function  $y=5f\left(x\right)$  .

• The graph of  $y=f\left(x\right)$ compressed horizontally by a factor of 1/5

• The graph of  $y=f\left(x\right)$  was stretched horizontally by a factor of 5

• The graph of  $y=f\left(x\right)$ was compressed vertically by a factor of 1/5

• The graph of  $y=f\left(x\right)$ was stretched vertically by a factor of 5

Which quadratic function is represented by the graph?

• $y=2\left(x-4\right)^2+5$

• $y=2\left(x+4\right)^2+5$

• $y=-2\left(x-4\right)^2+5$

• $y=-2\left(x+4\right)^2+5$

Tags

CCSS.HSF-IF.C.7A

The vertex of a function f(x) is (-4, 5). If $g\left(x\right)=f\left(x+2\right)$ , what is the vertex of $g\left(x\right)$  ?

• (-2, 5)

• (-6, 5)

• (-4, 3)

• (-4, 7)

Which of the following is the correct equation for the given graph?

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

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

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

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

Tags

CCSS.HSF-IF.C.7A

 $f\left(x\right)=\left(x-1\right)^2+5$  

What transformations have occurred?

• reflect over y-axis, left 1, up 5

• left 1, down 5

• reflect over x-axis, right 1, up 5

• right 1, up 5

Write an absolute value function given the following transformations:

Reflection across the x-axis

Vertical shift right 2 units

Horizontal shift down 7 units

• $f\left(x\right)=-\left|x+2\right|-7$

• $f\left(x\right)=\left|-x-2\right|-7$

• $f\left(x\right)=-\left|x-2\right|-7$

• $f\left(x\right)=-\left|x-2\right|+7$

• $f\left(x\right)=\left|-x+2\right|-7$

Identify the transformation from the graph of $f\left(x\right)=x^2$ to the graph   $g\left(x\right)=-\left(x+5\right)^2$ .

• shifted five units up and
  reflection in x-axis

• shifted five units down and
  reflection in x-axis

• shifted 5 units to the left and
  reflection x-axis

• shifted 5 units to the right and
  reflection x-axis

What is the equation of the quadratic function obtained from vertically stretching the parent function by a factor of 2 and then vertically shifting up 3 units?

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

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

• $f\left(x\right)=2x^2+3$
  

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

A function, $f\left(x\right)$ , has a domain of   $-4\le x\le6$  and a range of  $y\ge13$ . What are the domain and 

range of the function  $f\left(x+2\right)+5$  ?

•  $D:\ \left\{-6\le x\le4\ \right\}\ \ \ R:\ \left\{y\ge18\right\}$  

•  $D:\ \left\{-6\le x\le4\ \right\}\ \ \ R:\ \left\{y\ge8\right\}$  

•  $D:\ \left\{-2\le x\le8\ \right\}\ \ \ R:\ \left\{y\ge18\right\}$  

•  $D:\ \left\{1\le x\le11\ \right\}\ \ \ R:\ \left\{y\ge15\right\}$  

•  $D:\ \left\{1\le x\le11\ \right\}\ \ \ R:\ \left\{y\ge8\right\}$