Graphing Linear and Absolute Value Functions

The video tutorial explains how to graph an absolute value function, y = -1/4x + 1. It covers identifying transformations, such as vertical shrinking and horizontal stretching, and the effect of the negative sign on reflection over axes. The instructor demonstrates using a table of values to choose points that simplify calculations, avoiding fractions and decimals. The tutorial concludes with plotting points and understanding the graph's symmetry and transformations.

What is the first step in graphing an absolute value function?

• Finding the y-intercept

• Calculating the slope

• Drawing the x and y axes

• Identifying the vertex

What does the coefficient of x in the function y = -1/4x + 1 indicate?

• The graph will shift right

• The graph will be narrower

• The graph will be wider

• The graph will shift left

What is the new vertex of the function y = -1/4x + 1?

• (1, 0)

• (0, 1)

• (0, 0)

• (1, 1)

How does the graph of y = -1/4x + 1 compare to the graph of y = |x|?

• It is the same width and shifted left

• It is narrower and shifted down

• It is the same width and shifted right

• It is wider and shifted up

What is the effect of the 'plus 1' in the function y = -1/4x + 1?

• Shifts the graph left

• Shifts the graph right

• Shifts the graph up

• Shifts the graph down

How does a negative sign outside the absolute value affect the graph?

• Shifts the graph up

• Shifts the graph down

• Reflects over the x-axis

• Reflects over the y-axis

Why is it beneficial to use a table of values when graphing?

• To calculate the area under the curve

• To determine the y-intercept

• To find the slope

• To avoid using fractions and decimals

What is the y-value when x = -8 for the function y = -1/4x + 1?

• 1

• 4

• 2

• 3

What is the y-value when x = 4 for the function y = -1/4x + 1?

• 3

• 0

• 1

• 2

What is the significance of the graph's symmetry in absolute value functions?

• It simplifies the process of finding the y-intercept

• It indicates the graph will always be a straight line

• It allows for easier calculation of the slope

• It helps in predicting the graph's behavior on the opposite side