HW - 4.11 Transformations of Linear Functions

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

Which parent function matches the graph?

• f(x) = x

• f(x) = x²

• f(x) =2^x

• f(x) =|x|

If f(x) = 6x + 8 and g(x) = (6x + 8) + 2, what transformation occurred?

• Shifted (translated) up 2 units

• Shifted (translated) down 2 units

• Shifted (translated) left 2 units

• Shifted (translated) right 2 units

• Vertical stretch by a multiple of 2

If f(x) = 6x + 8 and g(x) = 6(x + 2) + 8, what transformation occurred?

• Horizontal stretch by a multiple of 2

• Shifted (translated) down 2 units

• Shifted (translated) left 2 units

• Shifted (translated) right 2 units

• Vertical stretch by a multiple of 2

If f(x) = 2x - 7 and g(x) = 5(2x - 7), what transformation occurred?

• Shifted (translated) up 5 units

• Shifted (translated) down 5 units

• Shifted (translated) left 5 units

• Shifted (translated) right 5 units

• Vertical stretch by a multiple of 5

If f(x) = 2x - 7 and g(x) = 2(x+5) - 7, what transformation occurred?

• Shifted (translated) up 5 units

• Shifted (translated) down 5 units

• Shifted (translated) left 5 units

• Shifted (translated) right 5 units

• Vertical stretch by a multiple of 5

If f(x) = 3x + 1 and g(x) = (3x + 1) + 4, what transformation occurred?

• Shifted (translated) up 4 units

• Shifted (translated) down 4 units

• Shifted (translated) left 4 units

• Shifted (translated) right 4 units

• Vertical stretch by a multiple of 4

If f(x) = 3x + 1 and g(x) = 4(3x + 1), what transformation occurred?

• Horizontal stretch by a multiple of 4

• Shifted (translated) down 4 units

• Shifted (translated) left 4 units

• Shifted (translated) right 4 units

• Vertical stretch by a multiple of 4

If f(x) = 3x + 1 and g(x) = 3(x - 4) + 1, what transformation occurred?

• Horizontal stretch by a multiple of 4

• Shifted (translated) down 4 units

• Shifted (translated) left 4 units

• Shifted (translated) right 4 units

• Vertical stretch by a multiple of 4

What kind of transformation is depicted:

g(x) = f(kx)

• Horizontal shift (translation)

• Vertical shift (translation)

• Horizontal stretch

• Vertical stretch