Precalculus Review - Transformations

The graph of this square root function has which type(s) of reflection:

 $y=-\sqrt{x-2}+1$  

I.  horizontal (over x-axis)

II. vertical (over y-axis)

• I only

• II only

• I and II
  

• Neither I nor II

Tags

CCSS.HSF-IF.C.7B

The graph of this cubic function has which type(s) of reflection:

 $y=-\left(2-x\right)^3+4$  

I.  horizontal (over x-axis)

II. vertical (over y-axis)

• I only

• II only

• I and II
  

• Neither I nor II

The constant "4" in the quadratic function:

 $y=4\left(x+1\right)^2-3$ 
produces: 

• A vertical stretch by a factor of 4

• A vertical compression by a factor of 1/4

• A horizontal stretch by a factor of 4
  

• A horizontal compression by a factor of 1/4

The constant "4" in the quadratic function:

 $y=\left(4\left(x+1\right)\right)^2-3$ 
produces: 

• A vertical stretch by a factor of 4

• A vertical compression by a factor of 1/4

• A horizontal stretch by a factor of 4
  

• A horizontal compression by a factor of 1/4

The translation point (TP) of the absolute value function is located at:

 $y=5-\left|3x+6\right|$ 

•  $\left(-2,\ 5\right)$  
  

•  $\left(2,\ 5\right)$  
  

•  $\left(-6,\ 5\right)$  
  

•  $\left(\frac{1}{2},\ 5\right)$  
  

Tags

CCSS.HSF-IF.C.7D

For which pair of functions are the graphs NOT identical?

•  $y=\sqrt{x+1}+1\ \ and\ \ \ y=\sqrt{-\left(x+1\right)}+1$  
  

•  $y=\left|x+1\right|+1\ \ and\ \ \ y=\left|-\left(x+1\right)\right|+1$  
  

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

•  $y=\frac{1}{\left(x+1\right)^2}+1\ \ and\ \ \ y=\frac{1}{\left(-\left(x+1\right)\right)^2}+1$  
  

For which pair of functions are the graphs NOT identical?

• $y=\sqrt{x-5}-5\ \ and\ \ \ y=-\sqrt{-\left(x-5\right)}-5$
  

• $y=\left(x-5\right)^3-5\ \ and\ \ \ y=-\left(-\left(x-5\right)\right)^3-5$
  

• $y=\left(x-5\right)^{\frac{1}{3}}-5\ \ and\ \ \ y=\left(-\left(x-5\right)\right)^{\frac{1}{3}}-5$
  

• $y=\frac{1}{x-5}-5\ \ and\ \ \ y=-\frac{1}{\left(-\left(x-5\right)\right)}-5$
  

Tags

CCSS.HSF-IF.C.7B

Which function is described by the graph shown?

(assume no stretches or compressions)

•  $y=-\sqrt{-\left(x-2\right)}+3$ 
  

•  $y=\sqrt{-\left(x-2\right)}+3$ 
  

•  $y=-\sqrt{\left(x-2\right)}+3$ 
  

•  $y=\sqrt{\left(x-2\right)}+3$ 
  

Tags

CCSS.HSF-IF.C.7B

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