Transformation of 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

If f(x) is the red graph and g(x) is the blue graph, what transformation changes f(x) to g(x)?

• translation

• rotation

• reflection

• vertical stretch

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

• Vertical stretch by a factor of 2

• Vertical compression by a factor of 1/2

• Vertical translation up by 2 units.

• Horizontal compression by a factor of 1/2

• Shrinks the graph vertically by a factor of 1/3 and translates up 4 units.

• Stretches the graph by a factor of 3 and translates up 4 units.

• Translates the graph left 1/3 of a unit and up 4 units.

• Translates the graph right 3 unites and down 4 units.

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

Edith graphed f(x) and g(x) = f(x + 1) on the same coordinate grid. Which statement describes how the graphs of f and g are related?

• The graph of the function f(x) is translated up 1 unit to produce g(x).

• The graph of the function f(x) is translated down 1 unit to produce g(x).

• The graph of the function f(x) is translated right 1 unit to produce g(x).

• The graph of the function f(x) is translated left 1 unit to produce g(x).

The graph of g is a ​ (a)   translation ​​ (b)   (c)   units of the graph of f.

• horizontal

• left

• vertical

• 3

• right

• up

• down

• 4

• 5

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

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 function’s graph is a translation of the graph of f(x) = x shifted 7 units to the left?

• a. g(x) = x − 7

• b. g(x) = −7x

• c. g(x) = 7x

• d. g(x) = x + 7