Exploring Transformations of Functions

This video tutorial covers the transformations of functions, including vertical and horizontal shifts, reflections, and stretching or shrinking of graphs. It explains how these transformations affect the position and shape of graphs on the coordinate plane. The tutorial also provides examples and exercises to help understand the application of these transformations in graphing functions.

What does a vertical transformation do to a graph?

• Reflects the graph over the y-axis

• Moves the graph up and down

• Stretches the graph horizontally

• Moves the graph left and right

If you add a value K to a function, what happens to the graph?

• It moves K units to the right

• It moves K units to the left

• It moves K units up

• It moves K units down

How do you move a graph H units to the right?

• Subtract H inside the parentheses with X

• Subtract H outside the parentheses with X

• Add H inside the parentheses with X

• Add H outside the parentheses with X

What is the new coordinate if a point (2, 6) is moved left 3 units and down 5 units?

• (-1, 11)

• (5, 1)

• (-1, 1)

• (5, 11)

What happens to the y-coordinates when reflecting over the x-axis?

• They are divided by -1

• They are added by 1

• They remain the same

• They are multiplied by -1

What is the effect of multiplying the function f(x) by a negative value?

• It reflects the graph over the y-axis

• It reflects the graph over the x-axis

• It stretches the graph vertically

• It shrinks the graph horizontally

What is the parent graph of y = -x^2 + 1?

• y = x^2

• y = -x^3

• y = -x^2

• y = x^3

What does a vertical stretch do to a graph?

• Moves the graph up and down

• Shrinks the graph towards the y-axis

• Moves the graph left and right

• Stretches the graph away from the x-axis

If a function is multiplied by a value greater than 1, what happens to the graph?

• It moves down

• It shrinks towards the x-axis

• It stretches away from the x-axis

• It moves up

What happens to the x-coordinates when reflecting over the y-axis?

• They remain the same

• They are multiplied by -1

• They are added by 1

• They are divided by -1