Families of Functions Transformations

The blue graph is the parent function f(x)=|x|, so the red must be...

• g(x)=|x+2|

• g(x)=|x|+2

• g(x)=|x-2|

• g(x)=|x|-2

• up

• flipped

• stretched

• compressed (shrink)

• down

• right

• left

• right

• down

• compressed (shrink)

• left

• flipped

• up

• stretched

Using your knowledge of transformations, match each graph to the equation it represents

• (x+4)² - 6

• 
• (x-4)² - 6

• 
• (x+4)² + 6

• 
• (x-4)² + 6

• 

The image shows a ​ (a)   translation ​ (b)   units ​ (c)  

• horizontal

• 4

• left

• vertical

• right

• 3

• up

The graph of g(x) is a
(a)   translation ​ (b)   units ​ ​ (c)   the graph.

• vertical

• 2

• 1

• up

• down

• left

• right

The graph of r(x) is a​ ​ (a)   ​by the graph of f(x) by a factor of ​ ​ (b)   .

• horizontal stretch

• horizontal shrink

• vertical stretch

• vertical shrink

• 1/3

• 3

• 2/3

Take the specified parent function and translate it left by 7 units, reflect it vertically, stretch it vertically by a factor of 2 units, then translate it 2 units up.

Mathematical Equivalence

ON

Take the specified parent function and translate it left by 7 units, reflect it vertically, stretch it vertically by a factor of 2 units, then translate it 2 units up.

Mathematical Equivalence

ON

Rewrite g(x) in translation form g(x) = f(x) + k

​ (a)   ​ ​ (b)   ​ (c)   ​

• g(x)=

• f(x)

• -11

• 7

• 9

• +11

• f(x)=