Transformations of Functions

Transformations of Functions

​Write this down!

Multiple Choice

 Describe the translation that occurred: $$m\left(x\right)=f\left(x+1\right)$$

• Left 1

• Right 1

• Up 1

• Down 1

Multiple Choice

Name the parent function.

• linear
• quadratic
• cubic
• logarithmic

Multiple Choice

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

Multiple Choice

Use the graphs of f and g to describe the transformation from the graph of f to the graph of g. (Hint: Look at the function g(x).)

• The graph of f is a vertical translation 4 units up from the graph g

• 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

Multiple Choice

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.

Multiple Choice

Describe the translation that occurred: $$w\left(x\right)=f\left(x-7\right)$$  

• Down 7

• Up 7

• Right 7

• Left 7

Multiple Choice

Describe the translation from the blue dotted graph to the red graph. (Hint: It moved 4 units left and 3 units down.)

• $$f\left(x-4\right)-3$$

• $$f\left(x-4\right)+3$$

• $$f\left(x+4\right)+3$$

• $$f\left(x+4\right)-3$$

Multiple Choice

How did the equation shift from the parent function? y = f(x - 4)

• Shift right by 4

• Shift left by 4

• Horizontal Stretch by 4

• Vertical Stretch by 4

• Shift down by 4

Multiple Choice

Which equation below is a quadratic function translated left 4 units?

• y = x² + 4
• y = (x + 4)²
• y = (x - 4)²
• y = 4x²

Multiple Choice

Which equation below is a quadratic that has been translated up 5 units?

(Hint: The parent function of a quadratic is y=x².)

• $$f\left(x\right)=x^2-5$$  

• $$f\left(x\right)=x^2+5$$  

• $$f\left(x\right)=\left(x-5\right)^2$$  

• $$f\left(x\right)=\left(x+5\right)^2$$  

• $$f\left(x\right)=\sqrt{x}+5$$  

Reflections of f(x)

When you see a negative in front of the function like -f(x), the function has been reflected across the x-axis or "flipped" upside down.

​

​The graphs shown are y=x² (red) and y=-x² (black).

Multiple Choice

Which transformation on

f(x) = x

is g(x) = -f(x)

• Reflection across the y-axis

• The slope will be less steep

• The graph will be wider

• Reflection across the x-axis.

Multiple Choice

Which function shows a reflection over the x-axis and a shift right 3 units?

• $$-f\left(x-3\right)$$

• $$-f\left(x+3\right)$$

• $$f\left(-x+3\right)$$

• $$-f\left(x\right)-3$$

Multiple Choice

$$-f\left(x+3\right)+4$$  

Describe the transformations:

• Shifted left 3 units
  Shifted up 4 units
  

• Reflection over the y-axis
  Shifted right 3 units
  Shifted up 4 units

• Shifted right 3 units
  Shifted up 4 units

• Reflection over the x-axis
  Shifted left 3 units
  Shifted up 4 units

Multiple Select

Describe the transformation: (click on two answers)

$$f\left(x\right)=-\left(x-7\right)^2$$  

• Reflection over the x-axis

• Reflection over the y-axis

• Shift 7 units left

• Shift 7 units right

Multiple Choice

Name the transformation from the function  $$y=\sqrt{x}$$   to the function   $$y=-\sqrt{x+3}$$  .

• Reflection over the y-axis, left 3.

• Reflection over the y-axis, right 3.

• Reflection over the x-axis, left 3.

• Reflection over the x-axis, right 3.