What you will learn today

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Presentation transcript:

What you will learn today 1. How to graph an absolute value function 2. How to determine the equation of an absolute value graph

Absolute Value Functions Use an x/y table to graph the following: y = |x| x y Objective: 2.8 Absolute Value Functions

Graphing Calculator Fun Let’s see how the graphs change as we add things to the equation. y = 2|x| y = -2|x| y = |x – 2| y = |x| + 2 Objective: 2.8 Absolute Value Functions

In Summary The graph of y = a|x – h| + k has the following characteristics: 1. The graph has vertex at (h, k) and is symmetric in the line x = h. 2. The graph is V-shaped. It opens up if a>0 and down if a<0. 3. The graph is wider than the graph of y = |x| if |a| < 1. The graph is narrower than the graph of y = |x| if |a| > 1. Objective: 2.8 Absolute Value Functions

Graphing an Absolute Value Function Graph y = |x+2| + 3 Safest way – Get the vertex from the equation. Use an x/y table. Objective: 2.8 Absolute Value Functions

You Try Graph y = |x – 2| - 3 Objective: 2.8 Absolute Value Functions

Another Example - Negative Graph: y = -|x – 1 | + 1 Objective: 2.8 Absolute Value Functions

You Try Graph y = -|x +2| + 3 Objective: 2.8 Absolute Value Functions

Example – Writing an Absolute Value Function Page 123. The vertex of the graph is (0, -3), so the equation has the form y = a|x – h| + k. Another point on the graph is (2, 1). 1. Substitute y = a|x – 0| + -3 2. Substitute the point (2, 1) for x and y in the equation and solve for a. 3. The equation is: Objective: 2.8 Absolute Value Functions

You Try Write an equation for the graph shown: Objective: 2.8 Absolute Value Functions

A “Real World” Example Y = -1.4|x – 2.5| + 3.5 The front of a camping tent can be modeled by the function: Y = -1.4|x – 2.5| + 3.5 Where x and y are measured in feet and the x-axis represents the ground. Graph the function and interpret the domain and range of the function in the given context. Objective: 2.8 Absolute Value Functions

Homework Page 126, 12-18 all, 20, 22, 26, 34, 36 How to use the graphing calculator. Objective: 2.8 Absolute Value Functions