11.8 Linear Transformations

$$g\left(x\right)=f\left(x\right)+4$$

$$g\left(x\right)=f\left(x\right)+5$$

$$g\left(x\right)=3f\left(x\right)$$

$$g\left(x\right)=\frac{1}{3}f\left(x\right)$$

$$y=x$$  

$$y=x^2$$  

$$y=x^3$$  

$$y=\sqrt[]{x}$$  

$$y=5x$$  is LESS STEEP than $$y=x$$  

$$y=5x$$  is STEEPER than $$y=x$$  

$$y=x$$ has the SAME slope as $$y=5x$$  

$$y=x$$  is STEEPER than $$y=5x$$  

$$y=\frac{3}{2}x$$  is STEEPER than $$y=x$$  

$$y=x$$  is STEEPER than $$y=\frac{3}{2}x$$  

$$y=\frac{3}{2}x$$  is LESS STEEP than $$y=x$$  

$$y=x$$  has the SAME slope as $$y=\frac{3}{2}x$$  

$$y=x-1$$  is STEEPER than $$y=x$$  

$$y=x-1$$  SHIFTED DOWN 1 unit from $$y=x$$  

$$y=x-1$$  is LESS STEEP than $$y=x$$  

$$y=x-1$$  SHIFTED UP 1 unit from $$y=x$$  

$$y=x+6$$  SHIFTED DOWN 6 units from $$y=x$$   

$$y=x+6$$  is STEEPER than $$y=x$$  

$$y=x+6$$  SHIFTED UP 6 units from $$y=x$$  

$$y=x+6$$  is LESS STEEP than $$y=x$$  

$$g\left(x\right)=f\left(x\right)+3$$  

$$g\left(x\right)=f\left(x\right)-3$$  

$$g\left(x\right)=3f\left(x\right)$$  

$$g\left(x\right)=-3f\left(x\right)$$  

Shifts the graph left 4 units

Shifts the graph right 4 units

Shifts the graph up 4 units

Shifts the graph down 4 units

Reflection across the y-axis

The slope will be less steep

The graph will be wider

Reflection across the x-axis.

g(x) is shifted up 6 units

g(x) is shifted down 6 units

g(x) is shifted left 6 units

g(x) is shifted right 6 units