CCSS.Math.Content.HSF-IF.C.7e
The standard
Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.
Common Core State Standards for Mathematics · Analyze functions using different representations
What this standard means
Students need to graph exponential, logarithmic, and trigonometric functions from equations and key features. They should identify intercepts, asymptotes, end behavior, period, midline, and amplitude, then use those features to sketch accurate graphs without relying only on a calculator.
Mastery looks like a labeled graph that matches the function’s structure and scale. Students often mix up horizontal and vertical shifts, forget that logarithms have vertical asymptotes, or use amplitude as the full height instead of half. For trig graphs, many struggle to connect the coefficient inside the function to the period.
Ways to teach it
- Hands-on activity: Give students equation cards and feature cards, then have them match each function to its intercepts, asymptote, period, or amplitude.
- Discussion prompt: Ask, “Which feature would you find first to sketch this graph, and why?” using one exponential, logarithmic, and trig example.
- Quick assessment: Show four graphs and four equations, then have students match them and write one feature that proves each match.
- Real-world connection: Model phone battery decay, sound waves, or earthquake magnitude, then have students identify the graph’s key features in context.
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Related standards
- CCSS.Math.Content.HSF-TF.B
Model periodic phenomena with trigonometric functions
- CCSS.Math.Content.HSF-IF.C.7a
Graph linear and quadratic functions and show intercepts, maxima, and minima.
- CCSS.Math.Content.HSF-TF.B.5
Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.
- 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...