Transformations of Functions Viviana C. Castellón East Los Angeles College MEnTe Mathematics Enrichment through Technology.

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Presentation transcript:

Transformations of Functions Viviana C. Castellón East Los Angeles College MEnTe Mathematics Enrichment through Technology

Absolute Value An Absolute Value graph is always in a “V” shape.

Given the following function, If: a > 0, then shift the graph “a” units up If: a < 0, then shift the graph “a” units down

Given the following function, Since a > 0, then shift the graph “3” units up

Let’s Graph

How will the graph look?

Let’s Graph

How will the graph look?

Let’s Graph

How will the graph look?

Let’s Graph

Given the following function, We get the expression (x - b) and equal it to zero x - b = 0 x = b If: b > 0, then shift the graph “b” units to the right If: b < 0, then shift the graph “b” units to the left

Given the following function, x – 1 = 0 x = 1 Since 1 > 0, then shift the graph “1” unit right

Let’s Graph

How will the graph look?

Let’s Graph

How will the graph look?

Let’s Graph

How will the graph look?

Let’s Graph

Graphing Recall: Shift “3” units up since 3 > 0 then we use the expression x + 1, and equal it to zero x + 1 = 0 x = -1 Since –1 < 0, then we shift “1” unit to the left

Let’s Graph

How will the graph look?

Let’s Graph

How will the graph look?

Let’s Graph

How will the graph look?

Let’s Graph

Given the following function, For this equation, c determines how wide or thin it will be. if: |c|>1, then the graph is closer to the y-axis if: |c|=1, then the graph remains the same if: 0<|c|<1, then the graph is further from the y-axis if c is a negative number, then the graph will reflect on the x-axis

Given the following function, Since |5| > 0, then the graph is closer to the y-axis

Let’s Graph

How will the graph look?

Let’s Graph

How will the graph look?

Let’s Graph

How will the graph look?

Let’s Graph

How will the graph look?

Let’s Graph

Given the following function, Since 4 > 0, shift the graph “4” units up x – 1 = 0 x = 1 Since 1 > 0, then shift the graph “1” unit to the right Since |5| > 0 shift the graph closer to the y-axis.

Let’s Graph

How will the graph look?

Let’s Graph

How will the graph look?

Let’s Graph

How will the graph look?

Let’s Graph

How will the graph look?

Let’s Graph

How will the graph look?

Let’s Graph

How will the graph look?

Let’s Graph

How will the graph look?

Let’s Graph

Congratulations!! You just completed the transformation of