Understanding Adding and Subtracting Rational Expressions

This video tutorial covers absolute value functions, starting with their basic properties and graphing techniques. It explains how to graph these functions using a table of values, focusing on the vertex and symmetry. The tutorial advances to graphing with transformations and handling cases where the vertex involves fractions. Finally, it explores piecewise functions that include absolute values and linear functions, detailing how to graph them effectively.

What is the notation for the absolute value function?

• f(x) = x + 2

• f(x) = 1/x

• f(x) = |x|

• f(x) = x^2

What shape does the graph of the parent absolute value function resemble?

• A straight line

• A parabola

• A V shape

• A circle

Where should the vertex be placed when creating a table of values for graphing?

• In the middle of the table

• At the beginning of the table

• It doesn't matter

• At the end of the table

What is the first step in finding the x-value of the vertex for an absolute value function?

• Set the x-value equal to one

• Set the y-value equal to zero

• Set the entire function equal to zero

• Set the expression inside the absolute value bars equal to zero

What is the domain of the parent absolute value function?

• All positive numbers

• All negative numbers

• All real numbers

• All integers

How do you ensure symmetry in the graph of an absolute value function?

• By using a calculator

• By centering the vertex and using equal increments on both sides

• By plotting only negative x-values

• By plotting only positive x-values

What should you do if the vertex of an absolute value function is a fraction?

• Use a calculator to find exact values

• Both B and C

• Ignore the fraction and use whole numbers

• Graph using fractional increments for accuracy

What is the range of the function f(x) = |2x + 6|?

• y ≤ 0

• y ≤ -6

• y ≥ 0

• y ≥ -6

How do you handle graphing piecewise functions with absolute values?

• Graph each piece separately and ensure continuity

• Graph only the absolute value part

• Ignore the linear parts

• Graph only the linear parts

What is the domain of a piecewise function with no gaps in x-values?

• All integers

• All real numbers

• All negative numbers

• All positive numbers