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Precalculus » A. Functions

  • A.1. Rectangular Coordinates

    1. A.1.M. Play Multiplayer 0 wins, 0 losses

    2. A.1.Q. Unit Challenge

    3. A.1.1. Plotting Points in the Cartesian Plane

      1. A.1.1.O. Overview
      2. A.1.1.1. Naming points using a graph
      3. A.1.1.2. Finding the coordinates of a point from a written description
      4. A.1.1.3. Determining the quadrant in which a point is located

    4. A.1.2. Scatter Plots

      1. A.1.2.O. Overview
      2. A.1.2.1. Using scatter plots to make predictions

    5. A.1.3. Finding Distances Using the Pythagorean Theorem

      1. A.1.3.O. Overview
      2. A.1.3.1. Find the distance between the two points
      3. A.1.3.2. Find the length of the side of the right triangle
      4. A.1.3.3. Show that the points form the vertices of a right triangle
      5. A.1.3.4. Word problems – Finding percent increase or decrease using a graph

    6. A.1.4. Finding the Midpoint of a Line Segment

      1. A.1.4.O. Overview
      2. A.1.4.1. Find the midpoint of the line segment between two points
      3. A.1.4.2. Word problems – predicting sales using the midpoint

    7. A.1.5. Translating Points in a Plane

      1. A.1.5.O. Overview
      2. A.1.5.1. Find the new coordinates of the translated polygon
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  • A.2. Equations, Graphs, and Symmetry

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    2. A.2.Q. Unit Challenge

    3. A.2.1. Determining Solution Points and Finding x-intercepts and y-intercepts

      1. A.2.1.O. Overview
      2. A.2.1.1. Determine if the point is a solution to the equation
      3. A.2.1.2. Finding intercepts using a graph
      4. A.2.1.3. Finding intercepts using an equation

    4. A.2.2. Testing for and Using Symmetry

      1. A.2.2.O. Overview
      2. A.2.2.1. Testing for symmetry with respect to the x-axis
      3. A.2.2.2. Testing for symmetry with respect to the y-axis
      4. A.2.2.3. Testing for symmetry with respect to the origin
      5. A.2.2.4. Complete the sketch of the graph using symmetry

    5. A.2.3. Equations of Circles

      1. A.2.3.O. Overview
      2. A.2.3.1. Write the equation of a circle given a center and radius
      3. A.2.3.2. Write the equation of a circle given a center and solution point
      4. A.2.3.3. Write the equation of a circle given two endpoints of a diameter
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  • A.3. Linear Equations in Two Variables

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    2. A.3.Q. Unit Challenge

    3. A.3.1. Finding and Using Slope

      1. A.3.1.O. Overview
      2. A.3.1.1. Tell whether the slope is positive, negative, zero, or undefined
      3. A.3.1.2. Estimate the slope of the line on a coordinate plane
      4. A.3.1.3. Find the slope and y-intercept of the equation
      5. A.3.1.4. Find the slope of the line passing through the given points

    4. A.3.2. Writing the Equation of a Line Using the Point-Slope Form

      1. A.3.2.O. Overview
      2. A.3.2.1. Write the equation of a line given a point and slope
      3. A.3.2.2. Write the equation of a line when the slope is undefined
      4. A.3.2.3. Write the equation of the line given two points

    5. A.3.3. Finding Parallel and Perpendicular Lines

      1. A.3.3.O. Overview
      2. A.3.3.1. Determine whether the lines are parallel, perpendicular, or neither given two equations
      3. A.3.3.2. Determine whether the lines are parallel, perpendicular, or neither given two sets of two points
      4. A.3.3.3. Write the equation of a parallel line given an equation and a point
      5. A.3.3.4. Write the equation of a perpendicular line given an equation and a point

    6. A.3.4. Using Slope as a Ratio and Rate of Change

      1. A.3.4.O. Overview
      2. A.3.4.1. Word problems – Tell whether the slope of the ramp meets the requirements
      3. A.3.4.2. Word problems – determine whether sales increased or decreased given a slope and find largest/smallest changes
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  • A.4. Functions

    1. A.4.M. Play Multiplayer 0 wins, 0 losses

    2. A.4.Q. Unit Challenge

    3. A.4.1. Determine whether the relation is a function

      1. A.4.1.O. Overview
      2. A.4.1.1. Determine whether a relation is a function using sets of ordered pairs

    4. A.4.2. Evaluating Functions

      1. A.4.2.O. Overview
      2. A.4.2.1. Evaluate the function using function notation
      3. A.4.2.2. Evaluate a piecewise function
      4. A.4.2.3. Finding the difference quotient

    5. A.4.3. Finding X-Values and the Domain of Functions

      1. A.4.3.O. Overview
      2. A.4.3.1. Find x-values for which the function is zero
      3. A.4.3.2. Find x-values for which two functions are equal
      4. A.4.3.3. Find the domain of the function given an equation

    6. A.4.4. Analyzing Graphs of Functions

      1. A.4.4.O. Overview
      2. A.4.4.1. Finding the Domain and Range of a Function Using a Graph
      3. A.4.4.2. Using the Vertical Line Test to decide if the Relation is a Function
      4. A.4.4.3. Finding the Zeros of a Function Algebraically
      5. A.4.4.4. Determining over Which Intervals the Function is Increasing, Decreasing, or Constant
      6. A.4.4.5. Finding the Relative Minimum and Relative Maximum of a Function
      7. A.4.4.6. Finding the Intervals for Which the Function is Positive
      8. A.4.4.7. Finding the Average Rate of Change of a Function
      9. A.4.4.8. Finding the Average Speed of an Object
      10. A.4.4.9. Determining if Functions are Even, Odd, or Neither
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  • A.5. Parent Functions and Transformations

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    2. A.5.Q. Unit Challenge

    3. A.5.1. Types of Functions

      1. A.5.1.O. Overview
      2. A.5.1.1. Parent Functions
      3. A.5.1.2. Piecewise Functions

    4. A.5.2. Types of Transformations

      1. A.5.2.O. Overview
      2. A.5.2.1. Graphing Vertical and Horizontal Shifts
      3. A.5.2.2. Graphing Reflections
      4. A.5.2.3. Graphing Vertical and Horizontal Stretches

    5. A.5.3. Writing Equations of Graphs Using Transformations

      1. A.5.3.O. Overview
      2. A.5.3.1. Write an equation given the described characteristics
      3. A.5.3.2. Write an equation using the graph
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  • A.6. Combinations of Functions and Composite Functions

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    2. A.6.Q. Unit Challenge

    3. A.6.1. Combinations of Functions

      1. A.6.1.O. Overview
      2. A.6.1.1. Find the sum and difference of two functions
      3. A.6.1.2. Find the product of two functions
      4. A.6.1.3. Find the quotient of two functions
      5. A.6.1.4. Word problems – combinations of functions

    4. A.6.2. Composite Functions

      1. A.6.2.O. Overview
      2. A.6.2.1. Composition of functions
      3. A.6.2.2. Evaluate using a composition of functions
      4. A.6.2.3. Find the domain of a composite function
      5. A.6.2.4. Decompose a function into two functions
      6. A.6.2.5. Word problems – composite functions
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  • A.7. Inverse Functions

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    2. A.7.Q. Unit Challenge

    3. A.7.1. Finding Inverses of Functions

      1. A.7.1.O. Overview
      2. A.7.1.1. Tell whether the graphs are inverses of each other
      3. A.7.1.2. Verify that two functions are inverse functions algebraically
      4. A.7.1.3. Find the inverse algebraically
      5. A.7.1.4. State the domain and range of a function and its inverse
      6. A.7.1.5. Word Problems – Finding inverse functions

    4. A.7.2. One-to-One Functions

      1. A.7.2.O. Overview
      2. A.7.2.1. Use a table to decide if a function has an inverse function
      3. A.7.2.2. Use the horizontal line test to determine if the inverse of a function is also a function
      4. A.7.2.3. Use the equation of a function to determine if it has an inverse function
      5. A.7.2.4. Restrict the domain of a function so that it has an inverse function
      6. A.7.2.5. Word Problems – One-to-one functions
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  • A.8. Mathematical Modeling and Variation

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    2. A.8.Q. Unit Challenge

    3. A.8.1. Modeling

      1. A.8.1.O. Overview
      2. A.8.1.1. Find a least squares regression line from a table of values

    4. A.8.2. Variation

      1. A.8.2.O. Overview
      2. A.8.2.1. Complete a table of values for a direct variation model
      3. A.8.2.2. Complete a table of values for an inverse variation model
      4. A.8.2.3. Determine whether a table shows direct or inverse variation and write the model
      5. A.8.2.4. Write a direct variation model given an x and y value
      6. A.8.2.5. Write a sentence using variation terminology to describe the formula
      7. A.8.2.6. Interest word problems
      8. A.8.2.7. Measurement word problems
      9. A.8.2.8. Tax word problems
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