Provide examples relevant to one’s life, family, or community that illustrate different situations in which quantities referenced are positive, negative, or an absolute value and justify.

Determine the distance of two real numbers of the form $±a,a∈R,$ from 0 on a number line, and relate this to the absolute value of a $(|a|)$.

Determine the absolute value of a real number.

Order, with justification, a set of real numbers that includes the absolute value of one or more of the quantities.

Explain, with the use of examples, how absolute value fits into the order of operations used on expressions involving real numbers.

Determine the value of numerical expressions involving absolute value(s).

Simplify expressions involving absolute value(s).

Analyze, describe, and explain the relationship between the graph of $y = f(x)$ and $y = |f(x)|$.

Create a table of values for $y = |f(x)|$ given $y = f(x)$.

Sketch the graph of $y = |f(x)|$ given $y = f(x)$ and explain the reasoning.

Develop and apply strategies for determining the intercepts, domain, and range of $y = |f(x)|$ given the equation of the function or its graph.

Explain what the range of the function $y = |f(x)|$ reveals about the graph of the function.

Develop, generalize, explain, and apply strategies for graphically determining (with and without the use of technology) the solution set of an equation involving absolute values of algebraic expressions.

Develop, generalize, explain, and apply strategies for algebraically determining the solution set of an equation involving absolute values of algebraic expressions.

Analyze and generalize conclusions about absolute value inequalities of the form $ |f(x)| < 0 $.

Identify and correct errors in a solution to an absolute value equation.

Solve situational questions involving absolute value functions or equations.

Analyze and generalize the relationship between $| x |$ and $√x^2$ and between $| f(x) |$ and $√(f(x))^2$.