Guided Lesson 5-4

Guided Lesson 5-4

Make sure you put ALL answers on your notes sheet!

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What to write on your paper: ​

1. Plug into DESMOS & copy the chart & the graph on your notes sheet.

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​2. Describe what happened to the graph.

Multiple Choice

​Based off what you did in the previous slide, what would be the equation for the blue line?

(Click on photo to enlarge)

Write the answer on your paper.

• $$f\left(x\right)=\left|x\right|-3$$  

• $$f\left(x\right)=\left|x\right|+5$$  

• $$f\left(x\right)=\left|x\right|+3$$  

• $$f\left(x\right)=\left|x\right|+2$$  

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What to write on your paper: ​

1. Plug into DESMOS & copy the chart & the graph on your notes sheet.

​

​2. Describe what happened to the graph.

Multiple Choice

​Based off what you did in the previous slide, what would be the equation for the blue line?

(Click on photo to enlarge)

Write the answer on your paper.

• $$f\left(x\right)=\left|x-1\right|$$  

• $$f\left(x\right)=\left|x+1\right|$$  

• $$f\left(x\right)=\left|x-3\right|$$  

• $$f\left(x\right)=\left|x+2\right|$$  

Multiple Choice

How much did the blue absolute value line move vertically?

• Shifted up 1.5

• Shifted down 1.5

• Shifted up 3

• Shifted down 3

Multiple Choice

What information does the constant h provide for the graph?

• Horizontal Shift

• Vertical Shift

Multiple Choice

If h is negative, which way is the graph shifting?

• Right

• Left

Multiple Choice

What information does the constant k provide for the graph?

• Horizontal Shift

• Vertical Shift

Multiple Choice

If k is positive, which way is the graph shifting?

• UP

• Down

Multiple Choice

How much did the blue absolute value line move horizontally?

• Shifted right 1.5

• Shifted left 1.5

• Shifted right 3

• Shifted left 3

Multiple Choice

How do you mathematically represent a vertical shift up?

• Adding to the output

  ex: $$f\left(x\right)=\left|x\right|+1$$  

• Subtracting to the output

  ex: $$f\left(x\right)=\left|x\right|-1$$  

Multiple Choice

How do you mathematically represent a horzontal shift to the right? (Be careful!!)

• Adding to the input

  ex:   $$f\left(x\right)=\left|x+1\right|$$  

• Subtracting to the input

  ex:   $$f\left(x\right)=\left|x-1\right|$$  

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​Refer back to last class period!

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​Use DESMOS to describe what happens to both equations.

​(Stretched or Compressed)

Multiple Choice

What happened to $$g\left(x\right)=\frac{1}{2}\left|x\right|$$  

• Graph was compressed. (Skinnier)

• Graph was stretched. (Wider)

Multiple Choice

What happened to $$g\left(x\right)=-4\left|x\right|$$  

• Graph was compressed. (Skinnier)

• Graph was stretched. (Wider)

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​Check your answers on the following slides.

Multiple Choice

For this equation: $$g\left(x\right)=-2\left|x+3\right|+4$$  was the equation stretched or compressed, and flipped or not flipped?

• Stretched & not flipped

• Compressed & not flipped

• Stretched & Flipped

• Compressed & Flipped

Multiple Choice

For this equation: $$g\left(x\right)=-2\left|x+3\right|+4$$  how was it shifted horizontally?

• Shifted right by 3 unites

• Shifted left by 3 unites

• Shifted right by 4 unites

• Shifted left by 4 unites

Multiple Choice

For this equation: $$g\left(x\right)=-2\left|x+3\right|+4$$  how was it shifted vertically?

• Shifted up by 3 unites

• Shifted down by 3 unites

• Shifted up by 4 unites

• Shifted down by 4 unites