# Interpreting recursive equations to write a sequence of transformations

Geometric shapes can be described by equations, making algebraic manipulation into a tool for geometric understanding, modeling, and proof. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities.

Decide if a specified model is consistent with results from a given data-generating process, e. For example, find a current data distribution on the number of TV sets per household in the United States, and calculate the expected number of sets per household.

Experiment with cases and illustrate an explanation of the effects on the graph using technology. Derive the equation of a parabola given a focus and directrix.

There are important results about all functions of a certain type — the factor theorem for polynomial functions, for example — and these require general arguments A. Recognize that there are data sets for which such a procedure is not appropriate. Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.

Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.

Write a function that describes a relationship between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association and nonlinear association. Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.

Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.

Understand the concept of a function and use function notation. Analytic geometry connects algebra and geometry, resulting in powerful methods of analysis and problem solving. Solve systems of equations. The same thinking — finding and articulating the rhythm in calculations — can help students analyze mortgage payments, and the ability to get a closed form for a geometric series lets them make a complete analysis of this topic.

Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.

Use given functions or choose a function suggested by the context. Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.

Interpret complicated expressions by viewing one or more of their parts as a single entity. Make sense of problems and persevere in solving them.

Look for and express regularity in repeated reasoning Algebra II is where students can do a more complete analysis of sequences F. Compute using technology and interpret the correlation coefficient of a linear fit.

As students acquire mathematical tools from their study of algebra and functions, they apply these tools in statistical contexts e. Construct a viable argument to justify a solution method. Common Core Standards for South Carolina Geometry An understanding of the attributes and relationships of geometric objects can be applied in diverse contexts—interpreting a schematic drawing, estimating the amount of wood needed to frame a sloping roof, rendering computer graphics, or designing a sewing pattern for the most efficient use of material.

Interpret the parameters in a linear or exponential function in terms of a context. Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.

Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. Explain and use the relationship between the sine and cosine of complementary angles.

Look for and express regularity in repeated reasoning. Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems e. Prove that all circles are similar. Understand statistics as a process for making inferences about population parameters based on a random sample from that population.

Construct viable arguments and critique the reasoning of others. For triangles, congruence means the equality of all corresponding pairs of sides and all corresponding pairs of angles. Geometry Overview Experiment with transformations in the plane Understand congruence in terms of rigid motions Prove geometric theorems Similarity, Right Triangles, and Trigonometry Understand similarity in terms of similarity transformations Prove theorems involving similarity Define trigonometric ratios and solve problems involving right triangles Apply trigonometry to general triangles Circles Understand and apply theorems about circles Find arc lengths and areas of sectors of circles Expressing Geometric Properties with Equations Translate between the geometric description and the equation for a conic section Use coordinates to prove simple geometric theorems algebraically Geometric Measurement and Dimension Explain volume formulas and use them to solve problems Visualize relationships between two-dimensional and three-dimensional objects Modeling with Geometry Apply geometric concepts in modeling situations Mathematical Practices 1.

Fundamental are the rigid motions: Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve which could be a line.Jun 09,  · What is a recursive formula, how do they generate sequences.

c. Graph transformations of basic functions including vertical shifts, stretches, and are studied because they are important for interpreting the world in which we live. The work with vertical shifts, stretches and shrinks, and reflections of graphs of basic functions is should be kept in a math notebook for ease in use.

Acquisition. Interpreting a graph *Creating a table of values *Working with functions Writing a linear equation *Using inverse operations to isolate variables and solve equations to show how the recursive sequence the sequence and the function f(x) = 2x + 5 (wh en x is a natural number) Write a function from a sequence or a sequence from a function.

a) Write an explicit formula for this sequence. b) Write a recursive formula for this sequence. Mrs. Kelly Ackerman. Untitled. About Mrs. Ackerman. Algebra II CP Calender. Algebra II CP Documents. Algebra II CP Documents.

Algebra II Syllabus. Calender. An understanding of the attributes and relationships of geometric objects can be applied in diverse contexts—interpreting a schematic drawing, estimating the amount of wood. Algebra I Notes Functions and Function Notation Unit 4 Functions and Function Notation Notes Page 3 of 22 9/10/ LEARNING TARGETS: To describe a relationship given a graph and to sketch a graph given a description.

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Interpreting recursive equations to write a sequence of transformations
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