Section 7 3 Graphs of Functions Graphs of

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

Standard Form • Example –Write 2 y + 3/2 = x in standard form • 2 y + 3/2 = x

Slope – Intercept Form • The Slope – Intercept Form is used for graphing the linear function. • Y = mx + b –m –b • 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 • 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 = -3 x - 1 –Y intercept –Slope – = = (0, -1) -3 = (-3/1) down 3 right 1 = (3/-1) up 3 left 1

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

Slope – Intercept form • Graph -3 y + 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 = 3 x – 3 • y = 3 x -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