Common Core Standards: Math
7. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
Next to magic tricks and juggling flaming torches, being able to sketch a graph just by looking at the equation is pretty much the coolest party trick around. We don't know what kinds of parties your students go to, but that's the gospel truth as far as we're concerned.
With all the different types of functions out there, knowing how to sketch them all is more than just a skill—it's a brag-worthy talent.
- Graph linear and quadratic functions and show intercepts, maxima, and minima.
- Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
- Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.
- Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.
- Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.