Functions and Transformations

Describe the transformation of y = f(x) for the new function
 y = f(x) + 5

• The graph of y = f(x) was shifted to the right 5 units. 

• The graph of y = f(x) was shifted to the left 5 units. 

• The graph of y = f(x) was shifted up 5 units. 

• The graph of y = f(x) was shifted down 5 units.

Describe the transformation of y = f(x) for the new function
 y = f(x) - 5

• The graph of y = f(x) was shifted to the right 5 units. 

• The graph of y = f(x) was shifted to the left 5 units. 

• The graph of y = f(x) was shifted up 5 units. 

• The graph of y = f(x) was shifted down 5 units.

Describe the transformation of y = f(x) for the new function
 y = 5f(x)

• The graph of y = f(x) compressed horizontally by a factor of 1/5

• The graph of y = f(x) was stretched horizontally by a factor of 5

• The graph of y = f(x) was compressed vertically by a factor of 1/5

• The graph of y = f(x) was stretched vertically by a factor of 5

Describe the transformation of y = f(x) for the new function
 y = 1/5f(x)

• The graph of y = f(x) compressed horizontally by a factor of 1/5

• The graph of y = f(x) was stretched horizontally by a factor of 5

• The graph of y = f(x) was compressed vertically by a factor of 1/5

• The graph of y = f(x) was stretched vertically by a factor of 5

Describe the transformation of y = f(x) for the new function
 y = - f(x)

• The graph of y = f(x) was flipped vertically across the x axis. 

• The graph of y = f(x) was flipped horizontally across the y axis.

• The graph of y = f(x) was shifted down.

• The graph of y = f(x) was shifted up

Describe the transformation of y = f(x) for the new function
 y = f(- x)

• The graph of y = f(x) was flipped vertically across the x axis. 

• The graph of y = f(x) was flipped horizontally across the y axis.

• The graph of y = f(x) was shifted down.

• The graph of y = f(x) was shifted up

Describe the transformation of y = g(x) for the function
y = 3g(x - 3) + 5

• Shifted up 5 units
  Shifted right 3 units
  Stretched vertically by a factor of 3

• Shifted up 5 units
  Shifted left 3 units
  Stretched vertically by a factor of 3

• Shifted down 5 units
  Shifted left 3 units
  Stretched vertically by a factor of 3

• Shifted down 5 units
  Shifted left 3 units
  Stretched vertically by a factor of 1/3

Identify the transformation from the graph of f(x)=x² to the graph g(x)= x² - 5

• shifted up five units

• shifted down five units

• shifted left five units

• shifted right five units

Identify the transformation from the graph of f(x)=x² to the graph g(x)= (x+5)² 

• shifted up five units

• shifted down five units

• shifted left 5 units

• shifted right 5 units

Identify the transformation from the graph of f(x)=x² to the graph g(x)= x² + 5

• shifted up five units

• shifted down five units

• shifted left five units

• shifted right five units