# Pre-Calculus Learning Targets

Math, Pre-Calculus

ALT 1 - Features of Functions

I can find features of functions in multiple forms.

**AST 1.1 - Identify Functional Relationships** : Identify functional relationships in multiple forms and use the forms to find information about the function.

**AST 1.2 - Use tech to find key features of functions** : Use technology to find key features of functions: intercepts, intervals where the function is increasing or decreasing, relative minimum and maximum, and end behavior.

**AST 1.3 - Determine Domain and Range** : Determine an appropriate domain and range for a function.

**AST 1.4 - Calculate-Interpret Rate of Change** : Calculate and interpret the average rate of change of a function over a specified interval, including estimating the rate of change from a graph.

**AST 1.5 - Construct Analyze Piecewise** : Construct and analyze piecewise defined functions graphically and symbolically.

**AST 1.6 - Construct Functions Contextualized Data** : Construct functions from contextualized data, including piecewise defined functions.

ALT 2 - New Functions

I can construct new functions represented in any form.

**AST 2.1 - Construct Function formed from Sum** : Construct the function formed from sum, difference, product or quotient of two functions.

**AST 2.2 - Construct Function Formed by Composition** : Construct the function formed by the composition of two functions.

**AST 2.3 - Construct the inverse of a function. ** : Construct the inverse of a function.

**AST 2.4 - Find Inverse of Function** : Find the inverse of any function and determine if the new relation is a function.

ALT 3 - Transformation of a Function

I can construct and explain the process of the transformation of a function of any form.

**AST 3.1 - Shift, Reflect Horizontally, Vertically** : Shift, reflect horizontally and/or vertically, and stretch horizontally and/or vertically a given function of any form.

**AST 3.2 - Construct and Investigate Transformation** : Construct and investigate the transformation of functions in the context of applications.

**AST 3.3 - Identify, Justify thinking** : Identify and justify my thinking in determining odd and even functions of any form.

ALT 4 - Exponential and Logarithmic Functions

I can analyze exponential and logarithmic functions and solve exponential and logarithmic equations.

**AST 4.1 - Exponential and Logarithmic Functions** : Represent exponential and logarithmic functions in a table, symbolically, verbally, graphically, and in context of applications.

**AST 4.2 - Express Logarithmic Func. Variety Bases** : Express logarithmic functions using a variety of bases (in addition to e and 10 as an inverse functions of exponential functions.

**AST 4.3 - Simplify Logarithmic Expressions** : Use properties of logarithms to simplify logarithmic expressions.

**AST 4.4 - Solve expon and logarithmic equations** : Solve exponential and logarithmic equations algebraically.

**AST 4.5 - Solve a Variety of Applied Problems** : Solve a variety of applied problems involving exponential and logarithmic functions.

ALT 5 - Polynomial Functions

I can analyze polynomial functions represented in a variety of forms.

**AST 5.1 - Rep a polynomial in a table and symbolic** : Represent a polynomial in a table and symbolically.

**AST 5.2 - Find and Estimate Zeros** : Find and/or estimate the zeros of a polynomial function and explain when it is not possible to find the exact zeros.

**AST 5.3 - Use and Apply Vocabulary** : Use and apply the vocabulary of polynomials including leading term, constant term, factored form, standard form, zeros, roots, solutions and the horizontal intercepts of a polynomial function.

**AST 5.4 - Sketch Polybomial Functions** : Sketch a polynomial function given the roots, corresponding multiplicity of the roots, and y-intercept without technology.

**AST 5.5 - Find Local Max, Min using Technology** : Find any local maximums and minimums using technology.

**AST 5.6 - Solve Applied Problems Rational Function** : *Solve a variety of applied problems involving polynomial functions.

ALT 6 - Rational Functions

I can analyze rational functions represented in a variety of forms.

**AST 6.1 - Find the End Behavior** : Find the end-behavior (horizontal asymptotes), vertical asymptotes, holes, zeros and the y-intercept, if any of these exist, of a rational function.

**AST 6.2 - Describe Asymptotic Behavior** : Describe the asymptotic behavior of a rational function verbally and with mathematical symbols.

**AST 6.3 - Represent Rational Function in Table** : Represent a rational function in a table, symbolically, verbally, graphically, and in context of application.

**AST 6.4 - Sketch Rational Function by Finding Root** : Sketch a rational function by finding the roots, corresponding multiplicity of the roots, y-intercept, and asymptotic behavior without technology.

**AST 6.5 - Identify Local Min, Max of Rational Func** : Identify any local minimums and maximums of a rational function using technology.

**AST 6.6 -Solve Applied Problems** : *Solve a variety of applied problems involving rational functions.

ALT 7 - Periodic Functions

I can define and evaluate periodic functions.

**AST 7.1 - Define Six Trigonometric Functions** : I can define the six trigonometric functions in terms of the sides of a right triangle and/or the unit circle.le.

**AST 7.2 - Evaluate Exact Values** : I can evaluate the exact values of the six trigonometric functions at 0 and integer multiples of Pi/6 pi/4 pi/3 pi/2 and pi

**AST 7.3 - Sketch an Angle in Standard Position** : I can sketch an angle in standard position, identify the initial and terminal rays, and identify the related or reference angle and co-terminal angle.

**AST 7.4 - Express Measure of Angle** : I can express the measure of an angle in degrees, and radians and convert from one form to another.

**AST 7.5 - Solve Problems Involving Arc Length** : I can solve problems involving arc length of a circle.

**AST 7.6 - Find the angle(s) given a ratio.** : Find the angle(s) given a ratio.

ALT 8 - Trigonometric Functions

I can analyze the transformation of trigonometric functions graphically, symbolically, numerically, verbally and within contextualized data exploration.

**AST 8.1 - Graph the sine, cosine and tangent funct** : Graph the sine, cosine and tangent functions.

**AST 8.2 - Graph Reciprocal Functions** : Graph the reciprocal functions - sec, csc, and cot.

**AST 8.3 - Identify Phase or Horizontal Shift** : Identify the phase shift or horizontal shift, amplitude, period, equation of the midline and vertical shift, and write the equation from the graph or draw the graph from the equation of a sinusoidal function.

**AST 8.4 - Fit a sinusoidal function** : Fit a sinusoidal function to data analytically using the concepts of horizontal shift, amplitude, period and midline.

**AST 8.5 - Investigate Mathematical Models** : Investigate mathematical models in the context of applications for sinusoidal functions.

ALT 9 - Trigonometric Identities

I can prove trigonometric identities and apply identities to find exact values.

**AST 9.1 - Use Pythagorean Simplify Expressions** : I can use the Pythagorean, reciprocal, co-function, sum and difference, double and half angle, and product to sum identities to simplify expressions.

**AST 9.2 - Solve Equations** : Use the Pythagorean, reciprocal, co-function, sum and difference, double and half angle, and product to sum identities to find new exact values.

ALT 10 - Solving Trigonometric Equations

I can solve trigonometric equations.

**AST 10.1 - Solve Problems Involving Right Triangle** : Find any number of solutions within a given restriction.

**AST 10.2 - Find exact solutions when possible. ** : Find exact solutions when possible.

**AST 10.3 - Find Approximate Solutions** : Find approximate solutions using the inverse trig functions when exact solutions are not possible.

ALT 11 - Angle Measure of Triangles

I can solve problems involving the angle measure and side length of right and oblique triangles.

**AST 11.1 - Solve problems involving right triangle** : Solve problems involving right triangles given two sides or a side and a non-right angle.

**AST 11.2 - Solve problems involving oblique triangles** : Solve problems involving oblique triangles using the Law of Sines, including the ambiguous case.

**AST 11.3 -Solve problems involving oblique triangles** : Solve problems involving oblique triangles using the Law of Cosines.

**AST 11.4 - Solve application problems** : Solve application problems involving right or oblique triangles.

ALT 12 - Vectors

I can solve problems using vectors.

**AST 12.1 - Describe vectors** : Describe vectors using magnitude and direction, and can resolve a vector into its vertical and horizontal components.

**AST 12.2 - Add and subtract vector** : Add and subtract vectors, and perform scalar multiplication both graphically and algebraically.

**AST 12.3 - Compute the dot product of two vectors** : Compute the dot product of two vectors.

**AST 12.4 - Use the dot product ** : Use the dot product to find the angle between two vectors.

ALT 13 - Parametric Equations

I can apply parametric equations to solve problems involving circular, elliptical motion and/or parabolic trajectories.

**AST 13.1 - Convert Parametric Rectangular** : I can convert from parametric form to rectangular form of equations and visa versa

**AST 13.2 - Write Equations Explicit Implicit** : I can write appropriate equations in explicit, implicit, and parametric form.

**Pre-Calculus AST.13.3** : I can write parameterizations of circles, ellipses and hyperbolas.

ALT 14 - Rectangular and Trigonometric Form

I can solve problems with complex numbers in both rectangular and trigonometric form.

**AST 14.1 - Plot Polar Coordinates** : Plot polar coordinates and create the graphs of polar functions.

**AST 14.2 - Convert complex numbers to different ** : Convert complex numbers to different forms: Cartesian, trigonometric, and exponential (using Euler’s formula).

**AST 14.3 - Complex Numb in Rectangular, Polar form** : Solve addition, subtraction, multiplication and division problems involving complex numbers in rectangular and polar form.

**AST 14.4 - Find an Nth Root of a Complex Number** : Find an nth root of a complex number.

ALT 15 - Communication

Communicates clearly and explains reasoning so others can follow how a problem is solved.

ALT 16 - Problem Solving

Reasons mathematically to solve problems using patterns and models in both a pure and applied context.