Review parent functions Graph Functions

by shiftsFind domain, range,

and intercepts

Day 5

Book Section 7.8

Get 2 grids for the 2 shift problems!

Domain: Range:

Y= Absolute Value Parent Function , ),0[

x y

-2 2

-1 1

0 0

1 1

2 2

Ex. 1

Domain: Range:

y=x2 Quadratic Parent Function , ),0[

x y

-2 4

-1 1

0 0

1 1

2 4

Ex. 2

Graph y = Domain:

Range:

,0 ,0

Ex. 3 Square Root Parent Function

x y

0 0

1 1

4 2

9 3

16 4

Domain: Range:

y=x3 Cubic Parent Function

Y scale: count by twos

, ,

x y

-2 -8

-1 -1

0 0

1 1

2 8

Ex. 4

Graph y = Domain:

Range:

,

,

Ex. 5 Cube root Parent Function

x y

-8 -2

-1 -1

0 0

1 1

8 2

Domain: Range:

f(x) = 122 x

Plot the parent function and shift each point:

Shift Left 2 and up 1

),2[ ),1[

x y

0 0

1 1

4 2

9 3

16 4

Shift using parent table and multiplying y values by 2

Ex. 6

Domain: Range:

f(x)= 462 3 x

Plot the parent function and shift each point:

Left 6 and down 4

),[ ),[

x y

-8 -2

-1 -1

0 0

1 1

8 2

Shift using parent table and multiplying y values by 2

Ex. 7

Shift coordinate:

Domain:

Range:

y-intercept:

x-intercept:

43)( 2 xxf

(3,-4)

(-∞,∞)

[-4,∞)

(0,5)

(5,0)

y=(0-3)2 – 4 y=(-3)2 – 4 y=5

0=(x-3)2 – 4

4=(x-3)2

4=x2-6x+90=x2-6x+50=(x-5)(x-1)

(1,0)

Ex. 8

Shift coordinate:

Domain:

Range:

y-intercept:

x-intercept:

482)( xxf

(-4,-4)

(-∞,∞)

[-4,∞)

(0,4)

(-2,0)

Y= – 4

y=40= – 4

4 =

2x+8 = 4 or 2x+8 = -4

x = -2 or x = -6

(-6,0)

802

Y= – 4 8

82 x

82 x

Ex. 9

Shift coordinate:

Domain:

Range:

y-intercept:

x-intercept:

12)( 3 xxf

(2,1)

(-∞,∞)

(-∞,∞)

(0,-7)

(1,0)

y=(0-2)3 + 1 y=(-2)3 + 1 y= -7

0=(x-2)3 + 1

-1=(x-2)3

Take cube root of both sides-1 = x – 2

x = 1

Ex. 10

Shift coordinate:

Domain:

Range:

y-intercept:

x-intercept:

(1,2)

(-∞,∞)

(-∞,∞)

(0,1)

(-7,0)

21)( 3 xxfEx. 11