Transformation of Function Graphs

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

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 4 units up from the graph f

• The graph of g is a horizontal translation of the graph of f, 4 units right

• The graph of g is a horizontal translation of the graph of f, 4 units left

• The graph of g is a vertical stretch of the graph of f, by a factor of 7

Which transformation will occur if f(x) = x is replaced with f(x) + 2?

• Translation left 2 units

• Translation right 2 units

• Vertical translation up by 2 units.

• Reflection across the x-axis.

What transformations occurred to get f(x), the red graph, to become g(x), the blue graph?

• horizontal shift down and vertical shift left

• horizontal shift left and vertical shift down

• horizontal shift right and vertical shift up

• horizontal shift up and vertical shift right

A student graphed f(x) = x + 1 and h(x) =f(x - 7) on the same graph. Which statement describes the graphs of f and h?​

The graph of f(x) ​ (a)   to create the graph of h.

• is shifted right 7 units

• is shifted up 7 units

• is shifted left 7 units

• is shifted down 7 units

• F

• G

• H

• J

A graph of g(x) is shown. Write an equation for g(x) as a transformation of the linear function f(x) = x.

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

• Graph g shifted down 3 units

• Graph g shifted down 4 units

• Graph g shifted up 4 units

• Graph g reflected

If the blue graph is
f(x) = x² 
then the red must be...

• g(x) = x² - 5

• g(x) = x² + 5

• g(x) = (x - 5)²

• g(x) = (x + 5)²

Which equation shows a function that is translated left 4 and 7 up?

• y = |x + 4| + 7

• y = (x - 4)² + 7

• y = (x + 7)² - 4

• y = |x + 4| - 7