Unit 2: Mid-Chapter Review

Unit 2:

Mid-Chapter Review

Sections 2.1-2.4

Transforming Linear Functions

On the next four slides, determine the transformations that occur to the linear parent function from the given equation.

Multiple Select

Describe the transformation of:  $g\left(x\right)=4\left(x-3\right)+5$  

[CHOOSE ALL THAT APPLY] 

• Vertical Stretch

• Vertical Shrink

• Reflect across the y-axis

• Translate Right

• Translate Up

Multiple Select

Describe the transformation of:   $h\left(x\right)=\left(4x-3\right)+5$  

[CHOOSE ALL THAT APPLY]

• Vertical Compression

• Horizontal Compression

• Shift Right

• Shift Left

• Shift Up

Multiple Select

Describe the transformation of:  $j\left(x\right)=-4\left(x-3\right)-5$ 

[CHOOSE ALL THAT APPLY]

• Reflect across the x-axis

• Vertical Stretch

• Vertical Shrink
  

• Translate Right

• Translate Down

Multiple Select

Describe the transformation of: $k\left(x\right)=\left(4x+3\right)-5$  


[CHOOSE ALL THAT APPLY]

• Vertical Shrink

• Horizontal Shrink

• Translate Left

• Translate Up

• Translate Down

Analyzing Linear Functions

You should be able to identify key attributes of linear functions such as the x-intercept, y-intercept, domain, and range.

Multiple Choice

Identify the x and y intercept of the linear function described by the equation and the graph: 

 $f\left(x\right)=\left(\frac{1}{2}x-4\right)$  

• x-int: (8, 0)
  y-int: (0, -4)

• x-int: (-8, 0)
  y-int: (0, 4)

• x-int: (0, 8)
  y-int: (-4, 0)

• x-int: (0, -8)
  y-int: (4, 0)

Multiple Choice

Identify the domain and range of the linear function described by the equation and the graph: 
 $g\left(x\right)=-\frac{1}{4}\left(4x+6\right)-5$  

• D:  $-\infty<x<\infty$  
  R:  $-\infty<y<\infty$  

• D:  $-\infty<y<\infty$  
  R:  $-\infty<x<\infty$  

• D:  $x\ge0$  
  R:  $y\ge0$  

• D:  $y>0$  
  R:  $x>0$  

Transforming and Analyzing Quadratic Functions

You should be able to identify key attributes of quadratic functions such as the x-intercept(s), y-intercept, domain, range and vertex.

Fill in the Blank

Identify the domain of the given equation:   $f\left(x\right)=\frac{1}{4}\left(x+2\right)^2-4$  

Domain: All ___________ Numbers

Fill in the Blank

Identify the range of the given equation:    $f\left(x\right)=\frac{1}{4}\left(x+2\right)^2-4$  
Range:  $y\ge$  ______

Multiple Choice

How many x-intercepts does the graph of the function  $k\left(x\right)=-\left(x-1\right)^2-9$  have?

• 0

• 1

• 2

• 3

Multiple Select

Describe what transformations of the quadratic parent function will result in the graph of the given function.

 $g\left(x\right)=-\left(2x-1\right)^2$    [CHOOSE ALL THAT APPLY]

• reflection across the x-axis

• horizontal stretch

• horizontal shrink

• shift right

• shift left

Transforming and Analyzing Cubic Functions

You should be able to identify key attributes of cubic functions such as the x-intercept(s), y-intercept, domain, and range.

Multiple Select

Describe what transformations of the cubic parent function will result in the graph of the given function.

 $g\left(x\right)=\left(2x-6\right)^3+1$    [CHOOSE ALL THAT APPLY]

• horizontal stretch
  

• horizontal shrink

• shift right

• shift up

• shift down

Multiple Choice

The domain and range of the function  $h\left(x\right)=\frac{1}{2}\left(x-2\right)^3-4$   is given as:       D: $\left\{x\ |\ x\inℝ\right\}$  and R:  $\left\{y\ |\ y\inℝ\right\}$  

What type of notation is being used?

• Inequality

• Interval

• Set-builder

Multiple Choice

Identify the x & y intercept of the given function:

   $h\left(x\right)=\frac{1}{2}\left(x-2\right)^3-4$  

• x-int: (-2, 0)
  y-int: (0, 8) 

• x-int: (0, -2)
  y-int: (4, 0)

• x-int: (-8, 0)
  y-int: (-4, 0)

• x-int: (4, 0)
  y-int: (0, -8)

Transforming and Analyzing

Absolute Value Functions

You should be able to identify key attributes of absolute value functions such as the x-intercept(s), y-intercept, domain, range, and vertex.

Multiple Choice

Identify the x & y intercept of the given function:

   $f\left(x\right)=\frac{1}{2}\left|2x-6\right|-5$  

• x-int: (-2, 0) and (8, 0)
  y-int: (0, -2) 

• x-int: (0, -2) and (0, 8)
  y-int: (-2, 0)

• x-int: none
  y-int: (-4, 0)

• x-int: none
  y-int: (0, -2)

Multiple Choice

The domain and range of the function  $f\left(x\right)=3\left|\frac{1}{2}x+1\right|+4$   is given as:       D: $\left(-\infty,\ \infty\right)$  and R:  $\left(-\infty,\ 4\right]$  

What type of notation is being used?

• Inequality

• Interval

• Set-builder

Fill in the Blank

Identify the vertex:   $g\left(x\right)=-\frac{3}{2}\left|x-1\right|+3$ 

 
*Hint*  $\left(\frac{c}{b},\ d\right)$  or use Desmos!