Section 7.2 Absolute Value Functions © Copyright all rights reserved to Homework depot: www.BCMath.ca

I) Review Line Equation: x y -4 -3 -2 -1 1 2 3 4 5 6 7 -5

Graphing Absolute Value Functions When graphing the absolute value of a function, any point with a negative y-coordinate will be positive If the point already had a positive y-coordinate, it will stay positive Only the Y-coordinate changes, the x-coordinate stays the same © Copyright all rights reserved to Homework depot: www.BCMath.ca

III) Graphs of Absolute Value Functions The ABS function will reflect any part of the function under the x-axis to above the x-axis The ABS of a straight line is a V-shape x y -4 -3 -2 -1 1 2 3 4 5 6 7 -5 The center of the graph is at the x-intercept The x-intercept is an “Invariant Point” a point that is not changed There are two sides: Left & Right Since the right side was reflected place the negative sign to the right piece wise function

Graph the function and: i) Determine the “x” and “y” intercepts ii) State the domain and range iii) State the piece-wise function x y -4 -3 -2 -1 1 2 3 4 5 6 7 -5 X-intercept: Y-intercept: Domain: Range:

Ex: Given the following parabola, graph the Absolute Value of this function: y -5 5 Take any part of the graph below the X-axis and vertically reflect it Note: Any number outside of the absolute value sign will be performed afterwards First take the abs of the parabola First shift the graph 4 units down Then shift the graph 4 units down Then take the abs of the parabola © Copyright All Rights Reserved Homework Depot www.BCMath.ca

Practice: Given the following graphs, draw the Absolute Value of each function: x y -5 5 x y -5 5 © Copyright All Rights Reserved Homework Depot www.BCMath.ca

Practice: Graph the following functions and then state the: i) X and Y intercepts ii) Domain and Range iii) Piece Wise Function

Graph Change the equation vertex form so it’s easier to graph Domain: Range: x y -4 -2 2 4 6 8 10 -6 X: Intercept: Y: Intercept:

Graph: X: Intercept: Y: Intercept: Domain: Range: x y -6 -4 -2 2 4 6 2 4 6 -5 5 X: Intercept: Y: Intercept: Domain: Range:

Graph: X: Intercept: Y: Intercept: Domain: Range: x y -4 -2 2 4 6 8 10 2 4 6 8 10 -6 X: Intercept: Y: Intercept: Domain: Range:

HW: Assignment 7.2

x y -4 -3 -2 -1 1 2 3 4 5 6 7 -5

x y -4 -3 -2 -1 1 2 3 4 5 6 7 -5