Transformations of Linear and Exponential Functions

Transformations of Linear and Exponential Functions

​

Linear Functions

• Start at the beginning: Negative sign in the front? Reflection.

• Number being multiplied in the front? Vertical stretch or shrink.

• Number being added or subtracted IN PARENTHESES? Shift left or right.

• Number being added or subtracted at the end? Shift up or down.

Multiple Select

 $f\left(x\right)=\frac{1}{2}\left(x-3\right)$  What transformations occurred? Check all that apply.

• Reflect over x-axis
  

• Vertical stretch

• Vertical shrink

• Shift left 3 

• Shift right 3

Multiple Select

 $f\left(x\right)=-3x+1$  What transformations occurred? Check all that apply.

• Reflect over x-axis

• Vertical stretch

• Vertical shrink

• Shift up 1

• Shift down 1

Multiple Choice

Which function matches the description? A linear function that has been reflected over the x-axis, shifted left 2, and shifted down 5.

• $f\left(x\right)=1\left(x-2\right)-5$

• $f\left(x\right)=-x+2-5$

• $f\left(x\right)=-\left(x+2\right)-5$

• $f\left(x\right)=\left(x-2\right)-5$

Exponentials

• Negative number in front? Reflection.

• Number multiplied IN FRONT? Vertical stretch or shrink.

• Number added or subtracted IN THE EXPONENT? Shift left or right.

• Number added or subtracted at the end? Shift up or down.

• GROWTH OR DECAY? Look at the number that has the exponent attached.

Multiple Select

 $f\left(x\right)=-\left(\frac{1}{3}\right)^x-4$  What transformations occurred? Check all that apply.

• Reflection over x-axis

• Shift up 4

• Shift down 4
  

• Exponential growth

• Exponential decay

Multiple Choice

Which function matches the description? An exponential function that was stretched by 3, shifted right 5, and has a growth factor of 2.

• $f\left(x\right)=2\cdot\left(3\right)^x-5$

• $f\left(x\right)=3\cdot\left(2\right)^{\left(x-5\right)}$

• $f\left(x\right)=2\cdot\left(3\right)^{\left(x+5\right)}$

• $f\left(x\right)=3\cdot\left(2\right)^x+5$