Internet MAT-117

Notes by Topic

 1. Cartesian Plane

  • Find distance between two points in the Cartesian Plane.
  • Use the Distance formula to solve Geometry and real-life application problems.
  • Find the Midpoint of the segment joining two points in the Cartesian Plane.
  • Use the Midpoint formula to solve application problem.


 2. Graphs of Equations

  • Determine whether a point lies on the graph of an equation.
  • Sketch graphs using a table of values and a graphing utility.
  • Find the x and y-intercepts of the graph of an equation (algebraically and graphically).
  • Determine the symmetry of the graph of an equation (algebraically and graphically).
  • Write the General Form Equation of a circle in Standard Form and determine the center and radius of the circle.

 Graphing Utilities

 3. Lines in the plane

  • Determine the slope of a line passing through two points.
  • Find the point-slope form equation of a line.
  • Find slope-intercept form equation of a line and sketch the line.
  • Determine if lines are parallel or perpendicular using slope.
  • Write equation of a line parallel or perpendicular to a given line.

4. Linear Modeling

  • Construct linear models.
  • Use linear models with slope as the rate of change.
  • Find a linear model that fits a set of data (Linear Regression).

 5. Functions

  • Determine if an equation or a set of ordered pairs represents a function.
  • Use function notation.
  • Evaluate a function.
  • Find the domain of a function.
  • Interpret input and output of Real-life functions.
  • Solve an application problem involving Real-life functions.

 6. Graphs of Functions

  • Find the domain and range using the graph of a function.
  • Vertical Line Test.
  • Describe the increasing and decreasing behavior of a function.
  • Classify a function as even or odd.
  • Identify six common graphs.

 7. Transformations of Functions

  • Describe how a graph has been changed from the original using common transformations.
  • Sketch the graph of a function using the common graphs and transformations.
  • Write the equation of a function using common graphs and transformations.

 8. Algebra of Functions

  • Find the sum, difference, product, and quotient of functions
  • Find the composition of two functions
  • Determine the domain of two combined functions
  • Determine the functions which have been composed to make up a given function
  • Solve real life problems involving the combination (addition, subtraction, multiplication, division, and/or composition) of two functions

 9. Inverse Functions

  • Determine if a function has an inverse function (Horizontal Line Test).
  • Find the Inverse of a function.
  • Graph a function and its Inverse.
  • Restricting the Domain to Create a Function with an Inverse Function

10. Quadratic Functions

  • Sketch the graph of a quadratic function (parabola) and identify its vertex and intercepts (algebraically and graphically).
  • Write a quadratic function in standard form and identify the vertex from the standard form.
  • Find the quadratic function given the vertex and a point on the graph
  • Solve real-life problems involving quadratic functions.

11. Polynomial Functions of Higher Degree

  • Classify polynomial functions as constant, linear, quadratic, cubic, etc.
  • Apply the Leading Coefficient Test to determine right and left behavior of the graph of a polynomial function
  • Find the real zeros of polynomial by factoring
  • Write the equation of a polynomial given its roots and a point on the graph.

12. Polynomial Division

  • Divide polynomials using long division.
  • Divise polynomials using synthetic division.
  • Use the Remainder Theorem to evaluate a polynomial.
  • Use the Factor Theorem to factor a polynomial.

 

 

13. Real Zeros of Polynomials

  • Find all possible rational zeros of a polynomial function using the Rational Zero Test.
  • Find all real zeros of a polynomial function algebraically.
  • Approximate the real zeros of a polynomial function using the Intermediate Value Theorem.
  • Approximate the real zeros of a polynomial using a graphing utility.
  • Write the equation of a polynomial given its roots and a point on the graph.

14. Rational Functions

  • Find the domain of a rational function.
  • Find the vertical and horizontal asymptotes of the graph of a rational function.
  • Sketch the graph of a rational function.
  • Use a rational function model to solve an application problem

15. Exponential Functions

  • Sketch the graph of an exponential function.
  • Find basic characteristics of an exponential function (domain, range, intercepts, increasing/decreasing behavior).
  • Write formulas of transformed exponential functions,
  • Use an exponential model to solve an application problem (in particular, models involving the natural exponential function and compound interest formulas).
  • Use the compound interest formula to solve finance problems.

16. Logarithmic Functions

  • Sketch the graph of a logarithmic function.
  • Investigate basic characteristics of a logarithmic function (domain, x-intercept, vertical asymptote).
  • Write formulas of transformed logarithmic functions.

17. Laws of Logarithms

  • Use the change of base formula to evaluate a logarithm.
  • Apply properties of logarithms.


18. Exponential and Logarithm Equations

  • Solve Logarithmic and Exponential Equations.


19. Exponential and Logarithm Models:

  • Use a logarithmic model to solve an application problem (in particular, models involving the natural logarithmic function).
  • Construct and use a model for exponential growth or exponential decay.

20. Systems in Two Variables - Substitution

  • Solve a linear system of equations by the method of substitution.
  • Solve a nonlinear system of equations by the method of substitution.
  • Construct and use a linear system of equations to solve an application problem.

21. Systems in Two Variables -Graphing

  • Solve a linear system of equations graphically.
  • Solve a nonlinear system of equations graphically.
  • Construct and use a linear system of equations to solve an application problem.

22. Systems in Two Variables -Elimination

  • Solve a linear system of equations by the method of elimination.
  • Construct and use a linear system of equations to solve an application problem.