Understanding Absolute Value and Transformations

The video tutorial covers solving absolute value equations and inequalities, transformations of functions, and their applications in real-world scenarios. It provides step-by-step instructions using graphing tools like Desmos, explains how to identify transformations such as shifts and reflections, and applies these concepts to practical examples like salary ranges and candy packaging. The tutorial concludes with a summary of key points and corrections of any typos made during the session.

What are the solutions to the equation |X + 8| - 5 = 2?

• -1 and -15

• -1 and 15

• 1 and -15

• 1 and 15

Which transformation occurs when subtracting a number outside the absolute value function?

• Shift left

• Shift right

• Shift up

• Shift down

How does a negative sign in front of an absolute value function affect its graph?

• Reflects over the x-axis

• Reflects over the y-axis

• Shifts up

• Shifts down

What is the effect of multiplying the absolute value function by a fraction between 0 and 1?

• Vertical compression

• Horizontal stretch

• Horizontal compression

• Vertical stretch

How does the graph of y = 1/2|x| + 3 differ from the parent function y = |x|?

• Narrower and shifted up

• Wider and shifted up

• Narrower and shifted down

• Wider and shifted down

What inequality represents a salary range that can differ by $1,560 from an average of $33,600?

• |x + 33,600| ≤ 1,560

• |x - 33,600| ≤ 1,560

• |x - 33,600| ≥ 1,560

• |x + 33,600| ≥ 1,560

If a bag of candy can be off by 8 pieces from 240, what is the correct inequality?

• |x + 240| ≥ 8

• |x - 240| ≥ 8

• |x + 240| ≤ 8

• |x - 240| ≤ 8

What is the average body temperature if it ranges from 98.2 to 99 degrees?

• 98.4

• 99.0

• 98.6

• 98.8

Which equation represents a graph shifted left 4, up 2, and reflected?

• |x - 4| - 2

• -|x - 4| + 2

• -|x + 4| + 2

• |x + 4| + 2

What is the solution set for the inequality 2|2x - 7| + 5 ≥ 23?

• x ≤ -1 or x ≥ 8

• x ≥ -1 or x ≤ 8

• x ≤ 1 or x ≥ -8

• x ≥ 1 or x ≤ -8