Chapter 4 Graphs and Transformations

Given the function in the form $y=af\left(b\left(x+c\right)\right)+d$  where the constants  $a$  , $b$  , $c$  and  $d$  will transform  $f\left(x\right)$  . Which constants are responsible for stretching the graph of the function?

•  $a$  

•  $b$  

•  $c$  

•  $d$  

What type of graph is shown above?

• linear

• quadratic

• cubic

• reciprocal

Which equation best describes the graph above?

• $y=-x^2$

• $y=-\frac{1}{x^2}$

• $y=-\frac{1}{x}$

• $y=\frac{1}{x^2}$

 Given the function in the form $y=af\left(b\left(x+c\right)\right)+d$ Which statement best describes the graph transformation as  $c$  increases?

• The graph will shift vertically up

• The graph will shift vertically down

• The graph will shift horizontally left

• The graph will shift horizontally right

Which of the following graphs represents $y=x^2\left(3-x\right)$  

• 
• 
• 
• 

Which function best decribes the transformation from purple to red?

• $y=f\left(x+1\right)+2$

• $y=f\left(x-1\right)+2$

• $y=f\left(x+1\right)-2$

• $y=f\left(x-1\right)-2$

 $P\left(0,\ 2\right)$ is a point on a function  $f\left(x\right)$  . After a transformation the point has moved to $P'\left(0,\ 6\right)$   . What transformation may have taken place?

•  $y=3f\left(x\right)$  

•  $y=f\left(3x\right)$  

•  $y=f\left(x+4\right)$  

•  $y=f\left(x\right)+4$  

 $f\left(x\right)$  is transformed by  $y=f\left(3x\right)$ . Which statement best describes the transformation.

• A vertical stretch of factor 3

• A vertical stretch of factor 1/3

• A horizontal stretch of factor 3

• A horizontal stretch of factor 1/3

 $f\left(x\right)=\frac{1}{x}$  is translated by the function  $y=f\left(x-3\right)+2$  What would be the asymptotes for the new graph?

•  $x=3$  

•  $x=-3$  

•  $y=2$  

•  $y=-2$  

The point $P\left(6,\ -8\right)$  lies on the graph of  $y=f\left(x\right)$ .

State the coordinates of the point to which P is transformed on the graph with equation  $y=-f\left(x\right)$  

•  $\left(6,\ -8\right)$  

•  $\left(-6,\ -8\right)$  

•  $\left(-6,\ 8\right)$  

•  $\left(6,\ 8\right)$