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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.

Graphing Parametric Equations

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Graphing Calculator Lesson (TI-84)

Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.

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.

Scientific Notation

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Graphing Calculator Lesson (TI-84)

Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.

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.

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.

Graphing Linear Equations on a Graphing Calculator

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Graphing Calculator Lesson (TI-84)

Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = –3x and the circle x² + y² = 3.

Graphing Polar Equations

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Graphing Calculator Lesson (TI-84)

Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number.

Calculating the Intersection Points for 2 Equations

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Graphing Calculator Lesson (TI-84)

Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = –3x and the circle x² + y² = 3.

Complex Number Operations

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Graphing Calculator Lesson (TI-84)

Know there is a complex number i such that i² = –1, and every complex number has the form a + bi with a and b real.

Solve quadratic equations with real coefficients that have complex solutions. N.CN.8 Extend polynomial identities to the complex numbers. For example, rewrite x2 + 4 as (x + 2i)(x – 2i).