Graph Functions by shifts Find domain, range, and intercepts

```Day 5
Book
Section
7.8
Ex. 1
Domain:
  ,  
Range:
x
y
-2
2
-1
1
0
0
1
1
2
2
[0,  )
Y= x Absolute Value Parent Function
Ex. 2
Domain:
  ,  
y=x2
Range:
x
y
-2
4
-1
1
0
0
1
1
2
4
[0,  )
Quadratic Parent Function
Ex. 3
Square Root Parent Function
Graph y =
x
y
0
0
1
1
4
2
9
3
16
4
x
Domain:
Range:
0 ,  
0 ,  
Ex. 4
Y scale: count by twos
Domain:
x
y
-2
-8
-1
-1
0
0
1
1
2
8
  ,  
Range:
  ,  
y=x3 Cubic Parent Function
Ex. 5 Cube root Parent Function
Graph y =
3
x
Domain:
Range:
  ,  
  ,  
x
y
-8
-2
-1
-1
0
0
1
1
8
2
Ex. 6
f(x) = 2 x  2  1
Shift Left 2 and up 1
Shift using parent table and
multiplying y values by 2
Plot the parent
function and shift
each point:
x
y
0
0
1
1
4
2
9
3
16
4
Domain:
[ 2,  )
Range:
[1,  )
Ex. 7
f(x)= 2
3
x64
Left 6 and down 4
Shift using parent table and
multiplying y values by 2
Plot the parent
function and shift
each point:
x
y
-8
-2
-1
-1
0
0
1
1
8
2
Domain:
[  ,  )
Range:
[  ,  )
Ex. 8
f ( x)  x  3  4
2
Shift coordinate:
Domain:
Range:
(-∞,∞)
[-4,∞)
y-intercept: (0,5)
x-intercept: (5,0)
(1,0)
(3,-4)
y=(0-3)2 – 4
y=(-3)2 – 4
y=5
0=(x-3)2 – 4
4=(x-3)2
4=x2-6x+9
0=x2-6x+5
0=(x-5)(x-1)
Ex. 9
f ( x)  2 x  8  4
Y= 2 0   8 – 4
Shift coordinate:
Domain:
Range:
(-4,-4)
(-∞,∞)
[-4,∞)
y-intercept: (0,4)
x-intercept: (-2,0)
(-6,0)
Y= 8 – 4
y=4
0= 2 x  8 – 4
4 = 2x  8
2x+8 = 4 or 2x+8 = -4
x = -2 or x = -6
Ex. 10
f ( x)  x  2   1
Shift coordinate:
Domain:
Range:
3
(2,1)
(-∞,∞)
(-∞,∞)
y-intercept: (0,-7)
x-intercept: (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. 11
f ( x) 
Shift coordinate:
Domain:
Range:
(1,2)
(-∞,∞)
(-∞,∞)
y-intercept: (0,1)
x-intercept: (-7,0)
3
x 1  2
```