Florida B.E.S.T. MA.912.AR.4.4
The Standard
Solve and graph mathematical and real-world problems that are modeled with absolute value functions. Interpret key features and determine constraints in terms of the context.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students represent situations with V-shaped functions, then solve for input or output values and graph the results. They explain what key graph features mean and limit the domain and range to values that fit the situation.
What Mastery Looks Like
- A student can write a function in the form y = a|x - h| + k from a situation and graph it over a reasonable domain. The student can find relevant solutions and explain the vertex, slopes, intercepts, domain, and range using units from the problem.
Common Misconceptions
- Students may graph only one branch, misread |x - h| as |x| - h, or place the vertex at the wrong sign. They may also use an unrestricted domain, treat the vertex as the y-intercept, or include solutions that make no sense in context.
How to Assess It
- Exit ticket: A roadside mechanic at mile 4 charges $5 plus $2 per mile traveled to a customer at x, where 0 ≤ x ≤ 10. Write and graph the cost function, find locations costing $11, and explain the vertex, slopes, domain, and range.
Lesson moves
Ways to Teach It
Stretch a string number line across the floor, mark a service center, calculate travel costs from location cards, and plot the ordered pairs.
Give two V-shaped cost graphs and ask students to explain which model fits a delivery scenario, using the vertex and slopes.
Run a card match with scenario cards, equations, graphs, solution points, and domain restrictions, then require partners to justify every match.
Map distances from the school along one road, write a transportation-cost function, and restrict its graph to the actual route.
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