Functions and Range Definitions

Give the vertex of the function, then graph.

State the domain and range for the function.

f(x) = |x| + 3

Vertex: ​ (a)  

Domain: ​ (b)  

Range: ​ (c)  

• (0, 3)

• (0, -3)

• (3, 0)

• x: {all Real numbers}

• x ≥ 3

• x ≤ 3

• y ≥ 3

• y ≤ 3

• y: { all Real numbers}

• y > 3

Tags

CCSS.HSF-IF.C.7D

Give the vertex of the function, then graph.

State the domain and range for the function .

f(x) = |x - 1| - 1

vertex: ​ (a)  

domain: ​ (b)  

range: ​ (c)  

• (1,-1)

• (-1, 1)

• (0, 0)

• (2, 0)

• {all real numbers}

• y ≥ -1

• x ≥ 1

Tags

CCSS.HSF-IF.C.7D

Match the definitions and pictures with the vocabulary

• Function Family

• a set of functions whose equations and graphs have a similar form and shape

• Absolute Value Functions

• 
• Parent Function

• 
• Linear Functions

• 
• Quadratic Functions

• the simplest function of the family

Write the function to transform the parent function for f(x) = |x| when the graph is shifted left 7 units.

• f(x) = |x + 7|

• f(x) = |x − 7|

• f(x) = 7|x|

• f(x) = -7|x|

• f(x) = |x| + 7

• f(x) = |x| − 7

Match the following vocabulary and definitions.

• Transformation

• flips a function

• Reflection

• turns a function about a point

• Rotation

• stretches or compresses a function

• Translation

• changes the position or size of a figure; can be applied to parent functions

• Dilation

• slides (or shifts) a function

Write the new function for the transformation: Vertically stretched by a factor of 5, then translated 1 unit left.

f(x) = ​ (a)   | x​ (b)   |

• 5

• + 1

• -5

• − 1

Write the new function for the transformation: Vertically stretched by a factor of 2, then translated 9 units down.

• 2

• + 0

• − 9

• -2

• + 9

• ½

• -½

Match the following parent functions with their graphs and equations.

• Absolute Value

• 
• Cubic

• 
• Linear

• 
• Exponential

• 
• Quadratic

• 

Describe how the following function compares

to the parent function f(x) = |x|

f(x) = -|x − 4|

• shifted right 4 units

• reflected over x-axis

• shifted left 4 units

• shifted up 4 units

• shifted down 4 units

Give the range of the set of ordered pairs: (2, 11), (9, -3), (7, 21), (-8, 6)

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.A.1