5/2/20151-9 parent functions1 warm_up #5 how do you think you did on the last test? what parts did...

04/21/23 1-9 Parent Functions 1

warm_up #5

• How do you think you did on the last test?

• What parts did you do well in?

• What parts could you have improved upon?

Grade Distribution

1st 3rd 7th A 7 4 6B 16 12 13C 4 6 4D 3 2 4F 0 5 3

No Show 1 2 1Avg 83.64 77.89 80.31


Introduction to Parent Functions

Section 1-9


What is a parent function?

• The parent function is the simplest function with the defining characteristics of the family. Functions in the same family are transformations of their parent function.


Parent Functions

(–∞, ∞)

[0, ∞)

(0, 0)

y-axis

Constant

f(x) = c

Family

Rule

Graph

Domain

Range

(–∞, ∞)

C

None

y-axis

(–∞, ∞)

(–∞, ∞)

(0, 0)

Origin

(–∞, ∞)

(–∞, ∞)

(0, 0)

Origin

Linear Quadratic Cubic

f(x) = x f(x) = x2 f(x) = x3

Zeros

Symmetry

|x x |x x |x x |x x

|y y c |y y | 0y y |y y


Parent Functions

Reciprocal

f(x) =

Family

Rule

Graph

Domain

Range

Zeros

Symmetry

1

x

[0, ∞)

[0, ∞)

(0, 0)

None

(–∞, ∞)

[0, ∞)

(0, 0)

y-axis

Squ Root Abs Value

f(x) = √x f(x) = |x|

(–∞, 0) U (0, ∞)

(–∞, 0) U (0, ∞)

None

Origin

| 0x x |x x | 0x x

| 0y y | 0y y | 0y y


Get some exercise


Example 1

Identify the parent function for g from its function rule. Graph g(x) on your calculator and describe what transformation of the parent function it represents. Then, identify the domain and range of the transformation.

( ) 3g x x

Linear Function, Down 3

Domain: (–∞, ∞)Range: (–∞, ∞)


Example 2


2( ) 2g x x

Quadratic Function, Shrinks with scale of 2 OR Horizontal Compression of 1/2

Domain: (–∞, ∞)Range: [0, ∞)


Example 3


2( )g x x

Quadratic Function, Reflection

Domain: (–∞, ∞)Range: (–∞, 0]


Your Turn


31( ) 2

2g x x

Cubic Function, Moves 2 units to the Right, Grows by a scale of 1/(Hor.

Stretch by 2 )

Domain: (–∞, ∞)Range: (–∞, ∞)


Example 4


( ) 4g x xSquare Root

Function, Reflection on x-axis,

Vertical Stretch

Domain: [0, ∞)Range: (–∞, 0]


Example 5

Determine from the data from this set of ordered pairs, describe the parent function, and the transformation that best approximates the data set.

x y

–2 2

–1 –1

0 –2

1 –1

2 2

Determine the equation and the slope

A) Graph it

B) If the ‘y’ difference and if ‘x’ are consistent:

…differs 1 time: LINEAR

…differs 2 times: QUADRATIC

…differs 3 times: CUBIC

More then two times, it can be EXPONENTIAL, CUBIC, or SQUARE ROOT


Example 5


2 ( 1) 3

x y

–2 2

–1 –1

0 –2

1 –1

2 2

( 1) ( 2) 1

2 ( 1) 1

( 1) 2 3

Linear

3 (1) 2

(1) ( 1) 2

1 ( 3) 2

Quadratic

Shift of Vertical down shift of 2


Example 6


x y

–2 –6

–1 1

0 2

1 3

2 10Cubic, Vertical Shift of 2


Your Turn


x y

0 0

1 1

2 1.414

3 1.732

4 2Square Root, No Shift


Assignment

Pg 71

3-27 odd, 39A-D

Know the Parent Function Chart

5/2/20151-9 parent functions1 warm_up #5 how do you think you did on the last test? what parts did...

Documents

parent functionssection

parent functionsreciprocalfx

function rule

quadratic function

cubic function

simplest function

linear function

square root function