Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available and showing end behavior.
Functions and Modeling
- Analyze functions using different representations.
Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available and showing end behavior.
Functions and Modeling
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graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.
graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
identify the effect on the graph of replacing ๐ง(๐น) by ๐ง(๐น) + ๐ฌ, ๐ฌ ๐ง(๐น), ๐ง(๐ฌ๐น), and ๐ง(๐น + ๐ฌ) for specific values of ๐ฌ (both positive and negative); find the value of ๐ฌ given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology.
compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
Graph rational functions, identifying zeros and asymptotes 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 rational functions, identifying zeros and asymptotes 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 rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.