This lesson unit is intended to help teachers assess how well students are able to: model a periodic situation, the height of a person on a Ferris wheel, using trigonometric functions; and interpret the constants a, b, c in the formula h = a + b cos ct in terms of the physical situation, where h is the height of the person above the ground and t is the elapsed time.
1. Write a function that describes a relationship between two quantities ?
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a. Determine an explicit expression, a recursive process, or steps for calculation from a context.
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b. Combine standard function types using arithmetic operations.
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c. (+) Compose functions.
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2. Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.?
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3. Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.
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4. Find inverse functions.
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a. Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse.
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b. (+) Verify by composition that one function is the inverse of another.
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c. (+) Read values of an inverse function from a graph or a table, given that the function has an inverse.
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d. (+) Produce an invertible function from a non-invertible function by restricting the domain.
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5. (+) Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.
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2. Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.
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Model with mathematics.
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Look for and make use of structure.
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