Transformations of Linear and Absolute Value Functions

This video tutorial covers transformations of linear and absolute value functions, focusing on horizontal and vertical shifts, as well as reflections over the x-axis and y-axis. The instructor provides detailed explanations and example problems to illustrate these concepts, helping students understand how to apply transformations to graphs.

What type of transformations are introduced in this lesson?

• Rotations

• Stretching and shrinking

• Horizontal and vertical shifts

• Translations and dilations

What happens to the graph of a function when it undergoes a horizontal transformation?

• It reflects over the y-axis

• It reflects over the x-axis

• It shifts left or right

• It shifts up or down

In a horizontal transformation, what does the graph of y = f(x - h) represent?

• A shift down by h units

• A shift to the right by h units

• A shift to the left by h units

• A shift up by h units

What is the effect of a vertical transformation on a graph?

• It reflects the graph over the x-axis

• It shifts the graph up or down

• It reflects the graph over the y-axis

• It shifts the graph left or right

If k is positive in a vertical transformation, in which direction does the graph move?

• Left

• Right

• Up

• Down

Given f(x) = 2x + 1, what is the function g(x) if the graph is translated 3 units down?

• g(x) = 2x - 3

• g(x) = 2x - 2

• g(x) = 2x + 4

• g(x) = 2x + 1

Given f(x) = 2x + 1, what is the function h(x) if the graph is translated 2 units to the left?

• h(x) = 2(x - 2) + 1

• h(x) = 2(x + 2) + 1

• h(x) = 2(x - 2) - 1

• h(x) = 2(x + 2) - 1

What does reflecting a graph over the x-axis do to the graph?

• It shifts the graph up

• It flips the graph left to right

• It flips the graph upside down

• It shifts the graph down

What is the result of reflecting the absolute value function y = |x| over the y-axis?

• The graph flips upside down

• The graph shifts down

• The graph shifts up

• The graph remains unchanged

Given f(x) = |x + 3| + 1, what is the function g(x) if the graph is reflected over the x-axis?

• g(x) = -|x + 3| + 1

• g(x) = |x - 3| + 1

• g(x) = |x + 3| - 1

• g(x) = -|x + 3| - 1