Comparing Graphs of a Linear Function and the
Square Root of the Linear Function
Linear Function
Square Root of a Linear Function
y  mx  b
y  mx  b
y  mx  b 
 x, y 
Domain:
Range:
 x | x 
 y | y 

y  mx  b
 x, y 
 x | mx  b  0
 y | y  0
Math 30-1
1
The Square Root of a Linear Function Characteristics
y  mx  b 
y  mx  b
For what values would a number and its square root be equal?
1 1
0 0
Invariant Points occur when y = 0 or y = 1
4 4
42
10  10
10  3.162
 x, 0 
4  4
4 is not defined
for real numbers
Math 30-1
 x,1
1
1

4
4
1
1

4
4
1 1

4 2
2
Graph the square root of y  2 x  4
x
-2x + 4
2 x  4
2
0
0
1
2
1.41
0
4
2
-1
6
2.45
-2
8
2.83
x 
2 x  4  0
2 x  4
x2
Domain:
Range:
y 
Invariant Points:
 y | y  0
y values of 0 or 1
(2, 0) and (1.5, 1)
Math 30-1
3
Observations from the Graph of a function and the Square root of the Function
Math 30-1
4
Comparing Graphs of a Quadratic Function and the
Square Root of the Quadratic Function
Quadratic Function
Square Root of a Quadratic Function
y  ax 2  bx  c
y  ax 2  bx  c
y  ax 2  bx  c  y  ax 2  bx  c
 x, y 
Domain:
 x | x 
Range:
 y | y  k

 x, y 
2
x
|
ax
 bx  c  0

 y | y  0
Math 30-1
5
Graphing the Square Root of a Function from a Graph of a Function
Domain
x  2
x  2
Range
y0
Invariant Points
y = 0 or 1
Sketch a curve
joining these
points above the
graph
Choose key points
 x, y 

 x, y 
Math 30-1
6
Graph the Square Root of a Function from a Graph of a Function
Compare the Domain, Range, and List any Invariant Points
y  f ( x)
x 
Domain:
Range:
 y | y  16
y
f ( x)
Domain:
Invariant Points:
 3, 0 
 2.9,1
 5, 0 
 4.9,1
Range:
Math 30-1
 x | 3  x  5
 y | 0  y  4
7
Page 86 – 89
Low: 2 – 8, 11
Medium:10, 12, 13
High: 14, 16, 17, 19
Math 30-1
8