Graphing Absolute Value Functions

The video tutorial introduces absolute value functions, explaining their properties and how to graph them using a table. It covers the concept of domain and range, and provides examples of graphing different absolute value functions. Advanced graphing techniques and variations are also discussed, helping students understand how changes in equations affect the graph's appearance.

What does the absolute value of a number represent?

• The square of the number

• The reciprocal of the number

• The negative of the number

• The distance from zero on the number line

What is the absolute value of -3?

• -1

• 3

• 0

• -3

When graphing an absolute value function, what shape does the graph typically take?

• A straight line

• A parabola

• A V shape

• A circle

What is the domain of the absolute value function f(x) = |x|?

• All integers

• All real numbers

• All negative numbers

• All positive numbers

How do you find the vertex of an absolute value function?

• Set the absolute value expression to zero

• Set the derivative to zero

• Find the maximum value of the function

• Find the minimum value of the function

What is the vertex of the function f(x) = |x - 4|?

• (0, 4)

• (4, 0)

• (-4, 0)

• (0, -4)

For the function f(x) = 2|x + 3|, what is the x-coordinate of the vertex?

• 0

• -3

• 3

• 2

How does the graph of f(x) = |x| + 5 differ from the graph of f(x) = |x|?

• It is shifted 5 units to the right

• It is shifted 5 units to the left

• It is shifted 5 units up

• It is shifted 5 units down

What effect does a negative sign in front of the absolute value have on the graph of the function?

• It shifts the graph to the left

• It shifts the graph to the right

• It reflects the graph over the x-axis

• It reflects the graph over the y-axis

What is the range of the function f(x) = -|x|?

• y < 0

• y ≥ 0

• y ≤ 0

• y > 0