How to Translate Linear Functions

This video tutorial covers the translation of linear functions, focusing on horizontal and vertical translations. It begins with an introduction to the concept of a parent function and how all linear functions are transformations of this basic function. The tutorial explains how horizontal translations affect the inputs (domain) and vertical translations affect the outputs (range) of a function. Through examples and practice problems, viewers learn to express these translations using function notation and understand the graphical implications of these transformations.

What is the parent function for linear functions?

• F(x) = x^2

• F(x) = 2x + 3

• F(x) = x - 1

• F(x) = x

How does a horizontal translation affect the graph of a linear function?

• It shifts the graph up or down.

• It reflects the graph over the x-axis.

• It changes the slope of the graph.

• It shifts the graph left or right.

In function notation, how is a horizontal translation represented?

• By dividing the output by a constant.

• By multiplying the input by a constant.

• By subtracting a constant from the input.

• By adding a constant to the output.

What happens to the graph of a function when a vertical translation is applied?

• The graph is reflected over the y-axis.

• The graph is shifted up or down.

• The graph is shifted left or right.

• The graph is stretched or shrunk.

How is a vertical translation expressed in function notation?

• By multiplying the output by a constant.

• By adding a constant to the input.

• By adding a constant to the output.

• By subtracting a constant from the input.

What is the result of a horizontal translation of F(x) = x when H is positive?

• The graph shifts right.

• The graph shifts down.

• The graph shifts left.

• The graph shifts up.

If a function is vertically translated by adding 3 to the output, what happens to the graph?

• It shifts 3 units to the left.

• It shifts 3 units to the right.

• It shifts 3 units up.

• It shifts 3 units down.

Why is function notation important in identifying the type of translation?

• It specifies the domain of the function.

• It determines the color of the graph.

• It indicates the direction of the translation.

• It shows the slope of the function.

In the exercise, what is the transformation when G(x) = F(x) - 8?

• Horizontal translation 8 units right

• Vertical translation 8 units up

• Horizontal translation 8 units left

• Vertical translation 8 units down

What is the correct function notation for a horizontal translation 5 units to the left?

• G(x) = F(x) - 5

• G(x) = F(x) + 5

• G(x) = F(x - 5)

• G(x) = F(x + 5)