Graphing Linear Functions and Absolute Values

The video tutorial explains how to graph absolute value functions and linear equations to find points of intersection. It begins with an introduction to graphing techniques, followed by a visual approach to graphing y = |x - 1|. The tutorial covers reflecting graphs across the x-axis and emphasizes the importance of labeling. It then demonstrates graphing y = 0.5x + 1, comparing slopes, and concludes with identifying intersection points to solve equations.

What is the primary technique used to solve the original equation in the video?

• Graphing the functions

• Using algebraic manipulation

• Substituting values

• Using a calculator

What does the graph of y = |x - 1| look like?

• A circle

• A straight line

• A parabola

• A V-shaped graph

How does the graph of y = x - 1 relate to y = |x - 1|?

• They are identical

• y = |x - 1| is a reflection of y = x - 1

• y = |x - 1| is a translation of y = x - 1

• y = |x - 1| is a rotation of y = x - 1

What happens to the graph of y = x - 1 when absolute value is applied?

• It remains unchanged

• It becomes a horizontal line

• It reflects over the y-axis

• It reflects over the x-axis

What is the result of reflecting the negative part of y = x - 1?

• It becomes y = x + 1

• It becomes y = 1 - x

• It becomes a vertical line

• It becomes a horizontal line

What is the y-intercept of the graph y = 0.5x + 1?

• -1

• 0

• 2

• 1

How does the slope of y = 0.5x + 1 compare to y = x - 1?

• It is inverted

• It is less steep

• It is the same

• It is steeper

What is the purpose of graphing both functions on the same set of axes?

• To determine their y-intercepts

• To see which is steeper

• To find points of intersection

• To compare their slopes

Why is the branch y = 0.5x - 1 irrelevant in finding intersections?

• It is a vertical line

• It does not intersect with the other graph

• It is parallel to the x-axis

• It is outside the graph range

What is the significance of labeling the branches of the graph?

• To identify the color of the graph

• To determine the length of the graph

• To calculate the area under the graph

• To easily identify points of intersection