Absolute Value Functions and Graphs Lesson 2-5. Important Terms Parent function: the simplest function with these characteristics. The equations of the.

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Absolute Value Functions and Graphs Lesson 2-5

Important Terms Parent function: the simplest function with these characteristics. The equations of the function in a family resemble each other, and so do the graphs. Offspring of parent functions include translations, stretches, and shrinks. Translation: it shifts a graph horizontally, vertically, or both. It results in a graph of the same shape and size but possibly in a different position Stretch: a vertical stretch multiplies all y-values by the same factor greater than 1, thereby stretching the graph vertically Shrink: a vertical shrink reduces y-values by a factor between 0 and 1, thereby compressing the graph vertically Reflection: in the x-axis changes y-values to their opposites. When you change the y-value of a graph to their opposites, the graph reflects across the x-axis (creates a mirror image)

The Family of Absolute Value Functions Vertical Translation Parent functionY=|x|Y=f(x) Translation up k units, k>0Y=|x|+kY=f(x)+k Translation down k units, k<0Y=|x|-kY=f(x)-k Horizontal Translation Parent FunctionY=|x|Y=f(x) Translation right h units, h>0Y=|x-h|Y=f(x-h) Translation left h units, h<0Y=|x+h|Y=f(x+k) Combined Translation (right h units, up k units)Y=|x-h|+kY=f(x-h)+k

Families of Functions: Absolute Value Functions Vertical Stretch or Shrink, and Reflection in x-axis Parent functionY=|x|Y=f(x) Reflection in x-axisY=-|x|Y= -f(x) Stretch (a>1)Y=a|x|Y=af(x) Shrink (0 { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://images.slideplayer.com/11/3170741/slides/slide_4.jpg", "name": "Families of Functions: Absolute Value Functions Vertical Stretch or Shrink, and Reflection in x-axis Parent functionY=|x|Y=f(x) Reflection in x-axisY=-|x|Y= -f(x) Stretch (a>1)Y=a|x|Y=af(x) Shrink (01)Y=a|x|Y=af(x) Shrink (0

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

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