# Activity: Graphing Absolute Value Functionsmrkuhlthau.weebly.com/uploads/9/4/4/2/9442708/graph_abs... · 2018. 10. 13. · Graphing Absolute Value functions on a TI83: You can find

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Activity: Graphing Absolute Value Functions

With a partner, complete the 2.8 Graphing Absolute Value Functions Activity.

You will need:• A partner• Activity sheet• Pencil• Graphing calculator

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1. Graph    using the following table of values

x y

2

10

1

2

Graph    using the following table of values:

x y

2

10

1

2

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Graphing Absolute Value functions on a TI83: You can find the absolute value function by accessing the Math key.  Arrow to the right to find the NUM menu.   On this screen you will find: #1  abs(  the absolute value function:

2. Graph   using your calculator and leave the equation in y  for the rest of the activity.

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3. THE EFFECT OF K:Graph the following functions and identify the vertex

a.  b.

Vertex_______________ Vertex_________________

Describe the effect of k on the graph:

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4. THE EFFECT OF h:Graph the following functions and identifya.  b.

Vertex_______________ Vertex_________________

Describe the effect of h on the graph:

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5. THE EFFECT OF a:Graph the following functions and identify the vertex:

a.  b.

Vertex_______________ Vertex_________________

c.  d.

Vertex_______________ Vertex_________________

Describe the two effects of a on the graph:

1.____________________________________________________

2.____________________________________________________

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6. Putting it all together…graph the following functions and identify the vertex.

a.  b.

Vertex_______________ Vertex_________________

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7. WITHOUT graphing, can you figure out the vertex of the following function?

Vertex_______________

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2.8 Graphing Absolute Value Functions

Graph

The graph is a piecewise function that consists of two rays and is V-shaped.

It opens up.

The corner point of the graph is called the vertex. In this case, it occurs at the origin.

Notice that the graph of is symmetric in the y-axis because for every point (x,y) on the graph, the point (-x,y) is also on the graph.

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General form of an absolute value function is y = a |x - h| + k

• The graph has vertex (h,k) and is symmetric in the line x = h

• The graph is V-shaped

• If a < 0, the graph opens down (a is negative)• If a > 0, the graph opens up (a is positive)

• 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

Note: When graphing, "a" is the slope to the RIGHT of the vertex

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For examples 1 & 2 tell if the graph opens up or down, and if it is narrower or wider. State the vertex.

Example 1: y = 6 |x - 7| Example 2: y = |x| + 9

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To graph y = a |x - h| + k

1. Plot the vertex (h,k)

2. Use the slope (a) to plot another point to the RIGHT of the vertex.

3. Use symmetry to plot a 3rd point

4. Complete the graph

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Graph y = - |x + 2| + 3

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Graph y = 2 |x - 1| + 1

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Example 3: Write the equation for

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Example 4: Write the equation for

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Take out your student handbook and write downthe homework assignment:

pg. 125-126 #12-17, 19-25 odd, 34-39

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