Absolute Value Functions and Inequalities

The video tutorial explains how to solve absolute value inequalities using a graphing calculator. It covers two examples, demonstrating how to graph the inequalities and find the solution intervals by identifying points of intersection. The tutorial emphasizes the use of interval notation and compound inequalities to express solutions.

What is the first step in solving absolute value inequalities using a graphing calculator?

• Solve the inequality by hand.

• Graph the left side as Y1 and the right side as Y2.

• Graph the inequality directly.

• Use the calculator's solve function.

What shape does the graph of an absolute value function typically take?

• A V-shape

• A parabola

• A circle

• A straight line

How do you access the absolute value function on a graphing calculator?

• Press the ALPHA key and then ABS.

• Use the function menu and select ABS.

• Press the ABS button directly.

• Press MATH, then right arrow, and select ABS.

What is the purpose of finding the points of intersection on the graph?

• To calculate the area under the curve

• To determine the slope of the line

• To find the x-coordinates where Y1 equals Y2

• To find the y-intercept

In the first example, what is the interval where Y1 is below Y2?

• From -3 to +3

• From -1 to +1

• From -5 to +2

• From -2 to +5

What does the inequality symbol '=' indicate in the second example?

• Y1 is on or above Y2

• Y1 is strictly above Y2

• Y1 is strictly below Y2

• Y1 is on or below Y2

What is the x-coordinate of the first point of intersection in the second example?

• 1.5

• 0.75

• -0.75

• -1.5

How is the solution interval expressed using interval notation for the second example?

• (-3/4, 7/4)

• [-3/4, 7/4]

• (-∞, -3/4) ∪ (7/4, ∞)

• (-∞, -3/4] ∪ [7/4, ∞)

Why is it important not to round non-terminating decimals when using interval notation?

• Rounding can lead to incorrect intervals.

• It makes the interval easier to read.

• Rounding is only necessary for large numbers.

• Decimals are always preferred over fractions.

What is the compound inequality representation for the solution in the second example?

• X < -3/4 and X > 7/4

• X > -3/4 and X < 7/4

• X = -3/4 or X = 7/4

• X = -3/4 and X = 7/4