Function Transformations and Stretch/Compression

Describe the stretch or compression in the function g(x) = 2x² compared to the parent function f(x) = x².

• No stretch or compression

• Vertical compression by a factor of 2

• Horizontal compression by a factor of 2

• Vertical stretch by a factor of 2

Explain the stretch or compression in the function k(x) = 0.5x compared to the parent function f(x) = x.

• Compression by a factor of 2

• Compression by a factor of 0.5

• No stretch or compression

• Stretch by a factor of 0.5

Describe the stretch or compression in the function q(x) = -3x² compared to the parent function f(x) = x².

• Compression by a factor of 2

• Compression by a factor of 3

• No stretch or compression

• Stretch by a factor of 3

Explain the stretch or compression in the function s(x) = 4x compared to the parent function f(x) = x.

• Stretch by a factor of 2

• Stretch by a factor of 4

• Compression by a factor of 4

• No stretch or compression

Which is a correct representation of the original function f(x) to its transformation g(x)?

• g(x)=-¼f(x)

• g(x)= -4f(x)

• g(x)= ¼f(x)

• g(x)=4f(x)

When k = 4, the graph of g is the graph of f​ ​​ ​ ​ ​ ​ ​ ​ ​ (a)   by a factor of 4

• stretched vertically

• compressed horizontally

• stretched horizontally

• compressed vertically

Use the graphs of f and g to describe the transformation from the graph of f to the graph of g.

• The graph of g is a vertical translation 2 units up of the graph of f

• The graph of f is a horizontal translation two units left of g

• The graph of g is a vertical stretch by a factor of 2 of the graph of f

• The graph of g is a reflection of the graph of f

A student graphed f(x) = x and g(x) = 4f(x). Which statement is true?

• The graph of f is steeper than the graph of g.

• The graph of f is less steep than the graph of g.

• The graph of f is shifted 2 units up to create the graph of g.

• The graph of f is shifted 2 units to the right to create the graph of g.

The graph shows the function f(x)=x² in blue and another function g(x) in red.  Which could be the equation for g(x)?

• g(x) = 2x²

• g(x) = 1/2x²

• g(x) = x² + 2

• g(x) = (x + 2)²

A student graphed f(x) = x and g(x) = 2f(x). Which statement is true?

• The graph of g is steeper than the graph of f.

• The graph of g is less steep than the graph of f.

• The graph of f is shifted 2 units up to create the graph of g.

• The graph of f is shifted 2 units to the right to create the graph of g.