Stretch and Shrinks

8

GOAL

• Understand what happens to a function when it is multiplied by a constant.

Investigate!• Complete the table below, then graph each

function on the same coordinate plane

x f(x) g(x)-2-1012

𝑓 (𝑥 )=𝑥2 g

Notes

• This is called a stretch because the y value increases for each value of x.

Investigate!

x f(x) g(x)-4-2-10124

𝑓 (𝑥 )=|𝑥| g

Notes

• This is called a shrink because the y value decreases for each value of x.

Adding onto our equation

a is called the “vertical stretch/shrink factor”

Note: If then it flipped over x-axis

Remember!

• All parent functions go through the point (1,1).• The value of a tells you the new point it will go

through.• Example: will go through the point (1,3)• Example: will go though the point ()

ExamplesAsk yourself: over 1, up?

• +2

Example: Write an equation

𝑦=𝑎 (𝑥−h )+𝑘

Zoom in

• Fill in the blanks

Homework

• All problems on Stretch/shrink worksheet