1. Section 7.3
Graphs of Functions

2. Graphs of Functions
In this section we are going to look at named graphs that are functions.
Names you will get very acquainted with are
Linear Function
Constant Equation
Absolute Value Function
Quadratic Function
Rational Function
Polynomial function

3. Linear Function
A function where the x value and y value do not have any powers.
A straight line graph, with no curves
Domain will ALWAYS be (-∞, ∞)
Range will ALWAYS be (-∞, ∞)
The three forms are
Standard Form Ax + By = C
Slope – Intercept Form y = mx + b
Point – Slope Form y - y₁ = m(x - x₁)

4. Standard Form Standard Form is used for future algebra problems.
Ax + By = C
Where A, B, C are all rational numbers, no fractions or decimals.
Where A needs to be a positive number.
Some problems will be
Addition Method CH 8
Matrix Method CH 8

5. Standard Form
Example
Write 2y + 3/2 = x in standard form
2y + 3/2 = x

6. Slope – Intercept Form
The Slope – Intercept Form is used for graphing the linear function.
Y = mx + b m
represents the slope
Needs to be written in a fraction form
Numerator is the up (+) and down (-) movement
Denominator is the right (+) and left (-) movement b
represents the y-intercept
(0, b)

7. Steps to Graph a Linear Equation
1. Write the equation is slope intercept form
2. Find the y-intercept, (0, b)
3. Plot the y-intercept (0,b).
4. Find the slope, m
Write m as a fraction
Numerator is the movement on the y-axis,
+ up, - down
Denominator is the movement on the x-axis,
+ right, - down
5. Use the slope to create your other points.
6. Connect all the points with a line.
7. Label one axis and put all 6 arrows in

8. Slope – Intercept form Graph y = (1/2) x + 2 Y intercept = (0, 2)
Slope = (1/2) up 1 right 2

9. Slope – Intercept form Graph y = -3x - 1 Y intercept = (0, -1)
Slope = -3 = (-3/1) down 3 right 1
= (3/-1) up 3 left 1

10. Slope – Intercept form
Graph y = -2x + 3
Y intercept =
Slope =

11. Slope – Intercept form
Graph -3y + x = - 9
Y intercept =
Slope =

12. Point – Slope form
Point – Slope form is used with word problems to find the equation of the line.
y - y₁ = m(x - x₁)
Point 1 (x ₁, y ₁) will change to values
Point 2 (x, y) left alone
Slope m will change to a value

13. Point - Slope Form Example
Find the equation of the line if the slope is 3 and it goes through the point (1, 2)
y - y₁ = m(x - x₁)
Point 1 (x ₁, y ₁) = (1, 2)
Point 2 (x, y)
Slope m = 3
y- 2 = 3(x-1)
y – 2 = 3x – 3
y = 3x -1

14. Point - Slope Form Example
Find the equation of the line if the slope is -2 and it goes through the point (-3, 1)
y - y₁ = m(x - x₁)
Point 1 (x ₁, y ₁)
Point 2 (x, y)
Slope m

15. Non-Linear Functions Constant Equation Absolute Value Function
Y = #
X = #
Absolute Value Function
f(x) = |x|
Quadratic Function
f(x) = x²
Rational Function
f(x) = 1 / x
Polynomial Function
High degree power…will see later in the semester

16. Constant function
A vertical or horizontal line through a given number.
Vertical Line will have the equation x = #
Horizontal Line will have the equation y = #

17. Vertical Line
Graph x = 2
Domain
Range

18. Horizontal Line
Graph y = 2
Domain
Range

19. Absolute Value Function
F(x) = |x|

20. Absolute Value Function
F(x) = |x|
Domain
Range

21. Quadratic Function
F(x) = x²

22. Quadratic Function
F(x) = x²
Domain
Range

23. Rational Function
F(x) = 1 / x

24. Rational Function
F(x) = 1 / x
Domain
Range

25. Homework
7, 9, 12, 15, 17, 20, 25, 32, 41, 46, 47, 64, 65