Absolute Value Function Investigation

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Absolute Value Function Investigation

The parent function is y = |x|. The vertex is the turning point of the graph. It is the maximum or minimum of the graph.

Remember: absolute value is a DISTANCE away from zero.

1)Graph each equation with the designated color. (You may want to lightly plot the points with pencil first, then use the colored pencil when you’re sure the points are correct.)

Graph each of the following and fill in the tables for each one.

y = |x| y = - |x|

Use tick marks on each grid line and count by 1’s.

1) Compare the graphs of y = |x| and y = - |x|. How are they the same and how are they different?

GROUP AGROUP B

1. y = |x|black1. y = |x| black

2. y = |x| - 2 blue2. y = |x| + 2 purple

3. y = |x| - 4 green3. y = |x| + 4 red

4. y = |x| - 6 orange4. y = |x| + 6 brown

Use tick marks on each grid line and count by 1’s.

Group A:

(1) In general, describe what happens to the graph of y = |x| when you subtract a number after the absolute value bars.

(2) State the vertex for each of the graphs. What connection can you make between the vertex and the equation? y = |x| -2 ( , ) y = |x| - 4 ( , ) y = |x| - 6 ( , )

Group B:

(1) In general, describe what happens to the graph of y = |x| when you add a number after the absolute value bars.

(2) State the vertex for each of the graphs. What connection can you make between the vertex and the equation? y = |x| + 2 ( , ) y = |x| + 4 ( , ) y = |x| + 6 ( , )

GROUP CGROUP D

1. y = |x|black 1. y = |x| black

2. y = |x + 2| blue2. y = |x – 2| purple

3. y = |x + 4| green3. y = |x – 4| red

4. y = |x + 6| orange4. y = |x – 6| brown

Use tick marks on each grid line and count by 1’s.

Group C:

(1) In general describe what happens to the graph of y = |x| when you add a number inside the absolute value bars.

(2) State the vertex for each of the graphs. What connection can you make between the vertex and the equation? y = |x + 2| ( , ) y = |x + 4| ( , ) y = |x + 6| ( , )

Group D:

(1) In general describe what happens to the graph of y = |x| when you subtract a number inside the absolute value bars.

(2) State the vertex for each of the graphs. What connection can you make between the vertex and the equation? y = |x - 2| ( , ) y = |x - 4| ( , ) y = |x - 6| ( , )

Group EGroup F

1. y = |x| black: x from - 3 to 31. y = |x| black: x from – 2 to 2

2. y = |2x| blue: x from -3 to 32. y = |½ x|purple: x use: - 4, -2, 0, 2, 4

3. y = |3x| green: x from -3 to 33. y = |1/3 x|red: x use: -6, -3, 0, 3, 6

4. y = |4x| orange: x from -3 to 34. y = |¼ x|brown: x use: -8, -4, 0 4, 8

Use tick marks on every other gridline on BOTHX-axis, use tick marks on every gridline and

axis and count by 1’s.count by 1’s. Y-axis place tick marks every

4th gridline and count by 1’s.

Group E:

(1) In general describe what happens to the graph of y = |x| when you multiply by a positive integer.

(2) What would happen if you multiplied by a negative integer?

(3) What is the vertex for all the graphs?

Group F:

(1) In general describe what happens to the graph of y = |x| when you multiply by a fraction between 0 and 1.

(2) What is the vertex for all the graphs?

Now that you have completed the investigation, use the equation y = -|2x + 5| -8 to describe in a short paragraph what each number does to the graph of y = |x| and what effect the negative has on the graph.

Using what you have learned from your investigation of the absolute value function, graph the following WITHOUT a table and WITHOUT a calculator. First graph y = |x| then graph the stated equation.

1) y = |x| - 12) y = |x +2|

3) y = |x + 2| - 44) y = - |x – 3| + 2

ReedCityHigh School – Sara Aubert, Brent Michell, Connie Banks, and Karen Shewan