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## Graphing Piecewise Defined Functions

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Graphing Calculator Lesson (TI-84)

Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

## Draw a Tangent Line of a Function

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Graphing Calculator Lesson (TI-84)

Construct a tangent line from a point outside a given circle to the circle.

## Numerically Calculate the Derivative of a Function

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Graphing Calculator Lesson (TI-84)

Calculating the derivatives of a function on a graphing calculator.

## Finding the Zeros of Functions

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Graphing Calculator Lesson (TI-84)

Factor a quadratic expression to reveal the zeros of the function it defines. 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.  Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

## Calculating Maximums/Minimums from a Graph of a Function

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Graphing Calculator Lesson (TI-84)

Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.

For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.

## Trig Functions using the Graphing Calculator

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Graphing Calculator Lesson (TI-84)

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.

## Graphing Trigonometric Functions

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Graphing Calculator Lesson (TI-84)

Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

## Plot the Graph of a Function within an Arbitrary Viewing Window

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Graphing Calculator Lesson (TI-84)

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.

Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

## Graphing Rational Functions

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Graphing Calculator Lesson (TI-84)

Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.

## Calculating a Value on the Graph of a Function

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Graphing Calculator Lesson (TI-84)

Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.  Read values of an inverse function from a graph or a table, given that the function has an inverse.