Download 7.3

Section 7.3
Graphs of Functions
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
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
–Slope – Intercept Form
–Point – Slope Form
Ax + By = C
y = mx + b
y - y₁ = m(x - x₁)
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
–Matrix Method
CH 8
CH 8
Standard Form
•Example
–Write 2y + 3/2 = x in standard form
•2y + 3/2 = x
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)
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
Slope – Intercept form
•Graph
y = (1/2) x + 2
–Y intercept
–Slope
=
=
(0, 2)
(1/2) up 1 right 2
Slope – Intercept form
•Graph
y = -3x - 1
–Y intercept
–Slope
–
=
=
(0, -1)
-3 = (-3/1) down 3 right 1
= (3/-1) up 3 left 1
Slope – Intercept form
•Graph
y = -2x + 3
–Y intercept
–Slope
=
=
Slope – Intercept form
•Graph
-3y + x = - 9
–Y intercept
–Slope
=
=
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)
–Point 2 (x, y)
–Slope m
will change to values
left alone
will change to a value
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
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
Non-Linear Functions
•Constant Equation
•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
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 = #
Vertical Line
•Graph x = 2
•
Domain
•
Range
Horizontal Line
•Graph y = 2
•
Domain
•
Range
Absolute Value Function
•F(x) = |x|
Absolute Value Function
•F(x) = |x|
•
Domain
•
Range
Quadratic Function
•F(x) = x²
Quadratic Function
•F(x) = x²
Domain
Range
•
Rational Function
•F(x) = 1 / x
Rational Function
•F(x) = 1 / x
•
Domain
•
Range
Homework
•7, 9, 12, 15, 17, 20, 25, 32, 41, 46, 47, 64, 65