Graphing Absolute Value Functions

The video tutorial covers graphing absolute value functions, focusing on the parent function y = |x| and its V-shaped graph. It explains how to translate these graphs by shifting them vertically and horizontally, affecting their domain and range. The tutorial also introduces piecewise and step functions, demonstrating how to model relationships using step functions. The video concludes with problem-solving examples, emphasizing the effects of constants on graph transformations.

What is the shape of the graph of an absolute value function?

• A circle

• A V-shape

• A parabola

• A straight line

What happens to the graph of y = |x| when it is shifted down by 2 units?

• The vertex moves to (0, 2)

• The vertex moves to (-2, 0)

• The vertex moves to (0, -2)

• The vertex moves to (2, 0)

What is the domain of the parent function y = |x|?

• x ≥ 0

• x ≠ 0

• x ≤ 0

• All real numbers

How does the range of y = |x| change when the graph is shifted up by 4 units?

• y ≤ 4

• y ≥ 4

• y ≥ -4

• y ≤ -4

What is the effect of adding a positive constant inside the absolute value function, such as y = |x + 3|?

• Shifts the graph down

• Shifts the graph up

• Shifts the graph to the left

• Shifts the graph to the right

What is the effect of subtracting a positive constant outside the absolute value function, such as y = |x| - 5?

• Shifts the graph to the right

• Shifts the graph down

• Shifts the graph to the left

• Shifts the graph up

What is a piecewise function?

• A function that is always decreasing

• A function with a single rule for its entire domain

• A function that has different rules for different parts of its domain

• A function that is always increasing

What does the graph of a step function resemble?

• A staircase

• A circle

• A straight line

• A V-shape

How many buses are needed if 61 students are going to a game, given each bus holds a maximum of 60 students?

• 4 buses

• 1 bus

• 2 buses

• 3 buses

What is the equation for translating the graph of y = |x| nine units up?

• y = |x| - 9

• y = |x - 9|

• y = |x + 9|

• y = |x| + 9