1. Lesson 10-5 Warm-Up

2. “Graphing Square Root Functions” (10-5)
What is a “square root function”? How do you find all of the solutions to a square root function?
Square Root Function: function, f(x), in which the independent variable, x, is inside a radicand Example: y = x (the simplest square root function) y = x + 3 y = 2x - 8 Since a radicand can’t be negative (you can’t square a negative value), the domain (x values) is limited to those values of x that make the radicand greater than or equal to zero. Therefore, you can create a function table to graph the solutions with x being values that make the expression inside the radicand greater than or equal to zero. To find the minimum value of the range, plug in the minimum value of x that will make the expression in the radical equal zero. Examples: Subtract 3 or add 8 to both sides Make a function table.

3. Find the domain of each function.
Graphing Square Root Functions
LESSON 10-5
Additional Examples
Find the domain of each function.
a. y = x + 5
x Make the radicand 0.
> –
x –5
> –
The domain is the set of all numbers greater than or equal to –5.
b. y = x – 12  
4x – Make the radicand 0.
> –
4x 12
> –
x 3
> –
The domain is the set of all numbers greater than or equal to 3.

4. “Graphing Square Root Functions” (10-5)
How do you graph a square root function?
To graph a square root function:
Make a function table with at least four x values. Make one of the x values the minimum value of x that makes the expression inside the radicand equal zero.
Plot the x and y value on the coordinate grid.
Connect the points to form a curve (should look like half of a parabola)
Examples:
Step 1. Function Table
Step 2. Plot the points.
Step 3. Connect the points to form a half parabola shape

5. Graphing Square Root Functions
LESSON 10-5
Additional Examples
The size of a television screen is the length of the screen’s diagonal d in inches. The equation d = 2A estimates the length of a diagonal of a television with screen area A.
Graph the function.
Domain
2A 0
A 0
> – 50
100
200
300
400 10
14.1 20
24.5
28.3
Screen
Area
(sq. in.)
Length of
Diagonal
(in.)

6. Graph y = x + 4 by translating the graph of y = x .
Graphing Square Root Functions
LESSON 10-5
Additional Examples
Graph y = x + 4 by translating the graph of
y = x .
For the graph y = x + 4,
the graph of y = x is shifted 4 units up.

7. Graph ƒ(x) = x + 3 by translating the graph of y = x .
Graphing Square Root Functions
LESSON 10-5
Additional Examples
Graph ƒ(x) = x + 3 by translating the graph of
y = x .
For the graph ƒ(x) = x + 3,
the graph of y = x is shifted to the left 3 units.

8. 1. Find the domain of the function ƒ(x) = 2x – 4. 2. Graph y = 3 x.
Graphing Square Root Functions
LESSON 10-5
Lesson Quiz
1. Find the domain of the function ƒ(x) = 2x – 4.
2. Graph y = 3 x.
3. Graph y = x – 3.
4. Describe how to translate the graph of y = x
to obtain the graph of the function y = x – 15.
x > 2
Shift the graph to the right 15 units.