Math 30-1
1
Graph a
Square Root
Function
Solving
Radical Eqn’s
Graphically
Radical
Functions
Graph the
Square Root of
a Function
Transformations
Math 30-1
2
What does square root mean?
2.1 Can you square root?
How can you estimate a square root
if the value is not a perfect square?
Write the equation for a square root function.f ( x ) 
x
Write the equation for the square root of a function.
How are these the same? Different?
Math 30-1
y
f  x
3
Use your calculator to create a table of
values of the following equations.
•
y = x2 and y = 𝒙
•
What do you notice about the
values in the two y-columns?
•
Why are all the y-values for
y = x2 positive?
•
Why do all negative x-values
produce an error for y = 𝒙 ?
x
4
2
0
-2
-4
y = x2
x
y= 𝑥
16
4
0
4
16
4
2
0
2
1.41
0
Error
Error
-2
-4
y=
2
x
and y = 𝒙
• What is the domain of y = x2 and
y= 𝒙?
– The domain of y = x2 is all real
numbers.
– The domain of y = 𝑥 is x ≥ 0.
• What is the range of y = x2 and y
= 𝒙?
– The range of y = x2 is y ≥ 0.
– The range of y = 𝑥 is y ≥ 0.
y = x2
x
y= 𝑥
2
0
-2
16
4
0
4
-4
16
4
2
0
-2
-4
2
1.41
0
Error
Error
x
4
Graphing y  x
Key Points
x
0
1
y
0
1
4
2
9
3
Are there any restrictions on the domain?
x | x  0
Range
 y | y  0
x- intercept
y- intercept
Math 30-1
6
Transformations of the Radical Function
y  k  a b( x  h)
y x
Which parameters affect the domain? Range?
Use a table of values to sketch the graph of y  x  3

y x
x
0
1
y
y  x3
0
1
x
-3
-2
y
0
1
4
2
1
2
9
3
6
3
Math 30-1
Domain?
 x | x  3  0
 x | x  3
Range?
 y | y  0
7
y x

y  x3
Translate the key points 3 units left.
Invariant Points?
Math 30-1
8
Math 30-1
9
Sketch the Graph using Transformations
y x
 y  2
x 1  3
Domain
 x | x  1
Range
 y | y  3
Invariant Points?
Math 30-1
10
Match each graph with its function equation
y  x4
y  x 4
y  x  2 1
y  2  x 1
Domain, Range, Invariant Points
Math 30-1
11
What falls faster a brick or a marble?
Galileo Galilei pondered this question
more than 400 years ago.
He theorized that the rate of falling
objects depends on air resistance, not on
mass. The result was they fell at the same rate.
Leaning Tower
of Pisa
Galileo
For objects falling near the surface of Earth, the function d = 5t2
approximately models the time, t, in seconds, for an object to
fall a distance, d, in metres, if the resistance caused by air can
be ignored. Express time as a function of distance.
d  5t 2 ,
d
 t2,
5
d

t
5
Is this correct?
Math 30-1
d
t
5
Restriction on the domain.
12
Consider the function
y = f(x)
Write an equation for the function in the form:
ya x
y  bx
1
y
x
2
1
y
x
4
Show algebraically that the two equations are equivalent.
2
1
y   x
2
y
1
y
x
4
y
Math 30-1
1
x
4
1
x
2
13