Exploring Absolute Value Equations and Inequalities

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

• A circle

• A V-shape

• A parabola

• A straight line

How is the absolute value function represented as a piecewise function?

• y = x for all x

• y = x for x > 0 and y = -x for x ≤ 0

• y = -x for x < 0 and y = x for x ≥ 0

• y = x for x < 0 and y = -x for x ≥ 0

What is the absolute value of -2?

• 4

• 2

• 0

• -2

How do you graph the absolute value of a linear function manually?

• Reflect the positive part below the x-axis

• Reflect the negative part above the x-axis

• Shift the graph to the right

• Shift the graph to the left

What are the possible number of solutions for an absolute value equation equal to a positive number?

• Two solutions

• Infinite solutions

• One solution

• No solutions

If the absolute value of x is equal to zero, how many solutions are there?

• Infinite solutions

• Two solutions

• One solution

• No solutions

What happens if an absolute value equation is set equal to a negative number?

• There are two solutions

• There is one solution

• There are no solutions

• There are infinite solutions

When solving absolute value inequalities, what does it mean if the inequality is 'less than'?

• There is no solution

• The solution is above the graph

• The solution is inside the interval

• The solution is outside the interval

For the inequality |5 - x| > 3, what is the solution set?

• x < 2 and x > 8

• x < 2 or x > 8

• x > 2 and x < 8

• x = 2 or x = 8

What is the first step in solving an absolute value inequality?

• Set the inequality to zero

• Isolate the absolute value expression

• Graph the function

• Multiply both sides by -1