Unit 2 Functions and Their graphs Pre Calculus

Unit 2 – Functions and Their graphs Pre- Calculus

1. 1 and 1. 2 INTERCEPTS, SYMMETRY, AND INTERPRETING GRAPHS

Recall Rectangular coordinate system Or xy – plane. X- intercepts – crosses x axis (y=0) Y – intercepts – crosses y axis (x=0)

Notes Determining whether a point is on a graph • Steps 1. Plug coordinates into given equation 2. Solve the equation. 3. Check that the two sides are equal If they are then, the point is on the graph If they are NOT then, the point is not on the graph

Example 1 I. Graph an equation by hand by plotting Points. a. Y = x 2 -4 We should expect the graph to look like: X Y -3 -2 -1 0 1 2 3 b. Would (10, 96) be on this graph?

Example 2 II. Find Intercepts from a graph. X- intercepts Y - intercepts

Notes Calculator Steps How to find intercepts with calculator How to find x and y intercepts algebraically How to find x intercepts using a calculator To find intercepts set the other variable equal to ZERO. Graph the equation Menu 6 -Analyze Graph 1 -Zero Click to the left and then to the right Zeros should pop up. -Need to find x intercepts, replace all y’s with zeros. -Need to find y intercepts, replace all x’s with zeros. How to find y intercepts using a calculator Graph the equation Menu 5 -Trace 1 -Graph Trace Get the cursor where the intercept should be and it pops up Enter

Example 3 II. Find intercepts from a graph using the calculator. a. y = x 3 -6 x 2 -13 x+4 X- intercepts: Y – intercepts: Sketch the graph

Example 4 III. Find intercepts algebraically. a. y = 2 x + 3 X- intercepts Y - intercepts b. y = x 3 – 64 X- intercepts Y - intercepts

Example 5

Examples of Symmetry x-axis symmetry y-axis symmetry Through the origin symmetry

Notes Symmetry A graph is considered symmetric with respect to the following if: the x-axis (x, y) ------ (x, -y) Is an equivalent equation? the y-axis (x, y) -----(-x, y) Is an equivalent equation? the origin (x, y)----- (-x, -y) Is an equivalent equation?

Example 8 ( , ) ( -2 , -1) ( a , -b )

Example 9 Decide if the following equation is symmetric with respect to the x-axis, y – axis, or origin. a. y = x 4 -2 x 2 – 8 x-axis y-axis origin

Common Functions

Pretty Number x -8 -2 0 2 8 y Intercepts: Symmetry:

Pretty Number x -4 -2 0 2 4 6 y Intercepts: Symmetry:

Pretty Number x -1 0 1 y Intercepts: Symmetry:

Pretty Number x -4 -2 0 2 4 6 y Intercepts: Symmetry:

Pretty Number x -2 -1 0 1 2 y Intercepts: Symmetry:

Pretty Number x 0 1 4 y Intercepts: Symmetry:

Pretty Number x -8 -1 0 1 8 y Intercepts: Symmetry:

Pretty Number x -2 -1 1 2 y Intercepts: Symmetry:

Pretty Number x y -2 Intercepts: -1 0 1 2 Symmetry:

Pretty Number x . 2 . 3 1. 2 1. 3 2. 2 2. 3 y Intercepts: Symmetry: