College Algebra

1. Linear Functions 1: I can
   • solve linear and absolute value equations in one variable.
2. Linear Functions 2: I can
   • solve linear and absolute value inequalities in one variable,
   • express the solutions to inequalities graphically,
   • express the solutions to inequalities using interval notation.
3. Linear Functions 3: I can
   • graph a line by plotting any two points on the line,
   • determine the slope of the line passing through two points in the plane,
   • write the equation of a line using Point-Slope Form,
   • write the equation of a line using Slope-Intercept Form.
4. Linear Functions 4: I can
   • determine whether two lines are parallel,
   • determine whether two lines are perpendicular,
   • find the equation of a line parallel to a given line,
   • find the equation of a line perpendicular to a given line.
5. Linear Functions 5: I can
   • determine whether a system of linear equations in two unknowns is consistent using either elimination or substitution.
   • determine whether a system of linear equations in three unknowns is consistent using either elimination or substitution.
   • determine whether a consistent linear system has a unique solution,
   • express the solutions to a dependent linear system as a set.
6. Quadratic Functions 1: I can
   • simplify square roots of negative numbers,
   • add complex numbers,
   • subtract complex numbers,
   • multiply complex numbers,
   • divide complex numbers.
7. Quadratic Functions 2: I can
   • solve quadratic equations by Completing the Square,
   • solve quadratic equations by Factoring,
   • solve quadratic equations using the Quadratic Formula,
   • solve quadratic equations using the Square Root Method.
8. Quadratic Functions 3: I can
   • find the vertex of a quadratic function,
   • find the x-intercepts of a quadratic function,
   • find the y-intercept of a quadratic function,
   • find the line of symmetry of a quadratic function,
   • graph a quadratic function.
9. Quadratic Functions 4: I can
   • use quadratic functions to solve minimization and maximization problems.
10. Rational Functions 1: I can
    • determine where a rational expression is undefined,
11. Rational Functions 2: I can
    • combine rational expressions using addition,
    • combine rational expressions using subtraction,
    • combine rational expressions using multiplication,
    • combine rational expressions using division,
    • simplify the rational expressions.
12. Rational Functions 3: I can
    • solve an equation involving rational expressions.
13. Rational Functions 4: I can
    • determine the asymptotes of a rational function and use this information to graph the function.
14. Rational Functions 5: I can
    • solve inequalities involving rational expressions.
15. Polynomial Functions 1: I can
    • solve general polynomial, polynomial-like, and quadratic-like equations.
16. Polynomial Functions 2: I can
    • understand the behavior of a polynomial function as the input values become large or large and negative,
    • graph a polynomial function from its factored form.
17. Polynomial Functions 3: I can
    • solve polynomial inequalities
18. The Cartesian Plane 1: I can
    • find the distance between two points in the plane,
    • find the midpoint between two points in the plane,
    • complete the square to put the equation of a circle into standard form,
    • translate between the standard form and the graph of the circle.
19. General Functions 1: I can
    • find the domain of a given relation,
    • find the codomain of a given relation,
    • find the range of a given relation,
    • determine whether the relation is a function.
20. General Functions 2: I can
    • evaluate a function at a given algebraic expression.
21. General Functions 3: I can
    • use transformations to graph a function.
22. General Functions 4: I can
    • use the graph of a function to determine the intervals where the function is increasing,
    • use the graph of a function to determine the intervals where the function is decreasing,
    • identify extreme values of a function.
23. General Functions 5: I can
    • determine whether a given function is odd,
    • determine whether a given function is even.
24. General Functions 6: I can
    • compose functions,
    • decompose functions,
    • identify the domain of a composition.
25. General Functions 7: I can
    • determine whether a given pair of functions are inverses of one another,
    • determine whether a function is one-to-one,
    • find the inverse of a one-to-one function,
    • use the graph of a one-to-one function to graph its inverse.
26. Other Functions 1: I can
    • solve equations involving rational exponents,
    • solve equations involving radical equations
27. Other Functions 2: I can
    • identify piecewise defined functions,
    • evaluate piecewise defined functions at points in the domain,
    • graph piecewise defined functions.
28. Exponential and Logarithmic Functions 1: I can
    • identify an exponential function,
    • find the domain of an exponential function,
    • find the range of an exponential function,
    • determine whether an exponential function represents growth or decay,
    • sketch a graph of an exponential function.
29. Exponential and Logarithmic Functions 2: I can
    • solve applications problems involving exponential functions.
30. Exponential and Logarithmic Functions 3: I can
    • identify a logarithmic function,
    • find the domain of a logarithmic function,
    • find the range of a logarithmic function,
    • sketch a graph of a logarithmic function
31. Exponential and Logarithmic Functions 4: I can
    • evaluate logarithmic functions at points in the domain,
    • use the change-of-base formula as necessary,
    • use the properties of logarithms to combine logarithmic expressions.
    • use the properties of logarithms to expand logarithmic expressions.
32. Exponential and Logarithmic Functions 5: I can
    • use the properties of exponentials to solve equations,
    • use the properties of logarithms to solve equations.