Linear Transformations

Compare the function

 $c\left(x\right)=x-3$  to the parent function $f\left(x\right)=x$  

• Vertical Translation Up 3 units

• Vertical Translation Down 3 units

• Vertical Stretch by a factor of 3

• Vertical Compression by a factor of 3

• Reflection over the x-axis

Compare the function

 $g\left(x\right)=x+5$  to the parent function $f\left(x\right)=x$  

• Vertical Translation Up 5 units

• Vertical Translation Down 5 units

• Vertical Stretch by a factor of 5

• Vertical Compression by a factor of 5

• Reflection over the x-axis

Compare the function

 $m\left(x\right)=2x$  to the parent function $f\left(x\right)=x$  

• Vertical Translation Up 2 units

• Vertical Translation Down 2 units

• Vertical Stretch by a factor of 2

• Vertical Compression by a factor of 2

• Reflection over the x-axis

Compare the function

 $p\left(x\right)=-4+x$  to the parent function $f\left(x\right)=x$  

• Vertical Translation Up 4 units

• Vertical Translation Down 4 units

• Vertical Stretch by a factor of 4

• Vertical Compression by a factor of 4

• Reflection over the x-axis

Compare the function

 $n\left(x\right)=\frac{1}{3}x$  to the parent function $f\left(x\right)=x$  

• Vertical Translation Up 1/3 units

• Vertical Translation Down 1/3 units

• Vertical Stretch by a factor of 1/3

• Vertical Compression by a factor of 1/3

• Reflection over the x-axis

Compare the function

 $h\left(x\right)=3+x$  to the parent function $f\left(x\right)=x$  

• Vertical Translation Up 3 units

• Vertical Translation Down 3 units

• Vertical Stretch by a factor of 3

• Vertical Compression by a factor of 3

• Reflection over the x-axis

Compare the function

 $z\left(x\right)=\frac{3}{2}x$  to the parent function $f\left(x\right)=x$  

• Vertical Translation Up 3/2 units

• Vertical Translation Down 3/2 units

• Vertical Stretch by a factor of 3/2

• Vertical Compression by a factor of 3/2

• Reflection over the x-axis

Compare the function

 $q\left(x\right)=x-2$  to the parent function $f\left(x\right)=x$  

• Vertical Translation Up 2 units

• Vertical Translation Down 2 units

• Vertical Stretch by a factor of 2

• Vertical Compression by a factor of 2

• Reflection over the x-axis

Compare the function

 $r\left(x\right)=\frac{1}{2}x$  to the parent function $f\left(x\right)=x$  

• Vertical Translation Up 1/2 units

• Vertical Translation Down 1/2 units

• Vertical Stretch by a factor of 1/2

• Vertical Compression by a factor of 1/2

• Reflection over the x-axis

Compare the function

 $t\left(x\right)=-4x$  to the parent function $f\left(x\right)=x$  

• Vertical Translation Up 4 units

• Vertical Translation Down 4 units

• Vertical Stretch by a factor of 4

• Vertical Compression by a factor of 4

• Reflection over the x-axis