Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
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