CCSS.Math.Content.HSF-IF.C.7b
The standard
Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
Common Core State Standards for Mathematics · Analyze functions using different representations
What this standard means
Students need to graph square root, cube root, absolute value, step, and other piecewise functions from equations, tables, or verbal rules. They should know the parent shapes, apply shifts and stretches, and handle domain limits, open circles, closed circles, and breakpoints.
Mastery looks like a clean graph with correct shape, key points, endpoints, and intervals. Students often mix up square root and cube root shapes, forget that square root needs a starting point, or graph both pieces of a piecewise rule outside their assigned intervals.
Ways to teach it
- Use graph paper and colored pencils to graph each piecewise rule one interval at a time, marking open and closed endpoints clearly.
- Ask students to explain how the graph of y equals square root of x minus 3 plus 2 changed from its parent function.
- Give four small graphs and have students match each to an equation, then circle the breakpoint or starting point.
- Show a taxi fare chart with a base fee and per-mile steps, then have students write and graph the step function.
Plan a lesson for CCSS.Math.Content.HSF-IF.C.7b
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Related standards
- CCSS.Math.Content.HSF-IF.C.7
Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
- CCSS.Math.Content.HSF-IF.C.7c
Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.
- CCSS.Math.Content.8.EE.A.2
Use square root and cube root symbols to represent solutions to equations of the form x² = p and x³ = p, where p is a positive rational number. Evaluate square ...
- CCSS.Math.Content.HSF-LE.A.2
Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pa...