Graphing Absolute Value Functions

The video tutorial explains how to graph an absolute value equation, specifically y = |3x - 6| + 1. It covers understanding the structure of absolute value equations, calculating the vertex, and applying transformations. The tutorial also demonstrates how to identify points on the graph using symmetry and discusses the effect of vertical stretching on the graph's steepness. The lesson concludes with a summary of the graphing process.

What is the equation being graphed in the tutorial?

• y = |x - 4| + 2

• y = |3x - 6| + 1

• y = |2x + 5| - 3

• y = |4x + 1| - 6

What is the role of the absolute value in the equation?

• To find the y-intercept

• To reflect the graph over the x-axis

• To ensure all y-values are positive

• To determine the slope

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

• Finding the y-intercept

• Understanding the equation's structure and transformations

• Plotting random points

• Calculating the slope

How do you find the x-coordinate of the vertex for the equation y = |3x - 6| + 1?

• Set x equal to 0

• Set 3x + 6 equal to 0

• Set 3x - 6 equal to 0

• Set 3x - 6 equal to 1

What is the significance of the vertex in an absolute value graph?

• It is the turning point

• It is the lowest point

• It is the highest point

• It is the midpoint

What is the new vertex of the graph after solving for x?

• (3, 1)

• (6, 1)

• (0, 1)

• (2, 1)

What is the effect of shifting the graph up by one unit?

• It changes the slope

• It changes the axis of symmetry

• It changes the y-coordinate of the vertex

• It changes the x-coordinate of the vertex

What happens to the graph when you change the value of k in y = |3x - 6| + k?

• It shifts vertically

• It stretches vertically

• It shifts horizontally

• It compresses vertically

What effect does the coefficient 3 have on the graph?

• It shifts the graph horizontally

• It reflects the graph over the x-axis

• It stretches the graph vertically

• It compresses the graph vertically

How do you determine the direction of the graph's opening?

• By the sign of the coefficient of x

• By the vertex

• By the y-intercept

• By the x-intercept