# College Algebra with Applications

**8.Perform computations with rational functions
Performance Standards**

Competence will be demonstrated:

8.a. by submitting all in-class and take home assignments with passing grades
according to the grading scale in the syllabus.

8.b. by participating actively in class discussions and activities.

Performance will be successful when:

8.a. you define a rational expression.

8.b. you recognize a rational expression.

8.c. you simplify rational expressions.

8.d. you add, subtract, multiply and divide rational expressions.

8.e. you simplify complex fractions.

8.f. you define a rational function and the domain of a rational function.

8.g. you find vertical, horizontal, and oblique asymptotes.

8.h. you discuss the properties of f (x) = 1/x, graph it and apply
transformations to rational functions.

8.i. you determine the behavior of rational functions as the absolute value of
the variables becomes large.

8.j. you identify removable discontinuities.

8.k. you determine the end behavior for rational functions where the degree of
the numerator does not exceed the degree of the denominator .

8.l. you graph rational functions.

8.m. you solve rational functions algebraically and graphically .

8.n. you discuss extraneous solutions.

**9.Perform computations with radical functions
Performance Standards**

Competence will be demonstrated:

9.a. by submitting all in-class and take home assignments with passing grades
according to the grading scale in the syllabus.

9.b. by participating actively in class discussions and activities.

Performance will be successful when:

9.a. you define radical, index, and radicand.

9.b. you define principal square root , cube root, nth root.

9.c. you determine the domain of radical expression.

9.d. you solve radical equations algebraically and check for extraneous roots.

**10.Analyze exponential and logarithmic functions
Performance Standards**

Competence will be demonstrated:

10.a. by submitting all in-class and take home assignments with passing grades
according to the grading scale in the syllabus.

10.b. by participating actively in class discussions and activities.

Performance will be successful when:

10.a. you define base and exponent.

10.b. you define the exponential function with base 10, base 2, fractional base,
an arbitrary base, and base e.

10.c. you graph the exponential function with base 10, base 2, fractional base,
an arbitrary base, and base e.

10.d. you apply transformations to exponential functions.

10.e. you apply exponential functions to such problems as exponential growth and
decay, half-life, interest, annuities, and mortgages.

10.f. you solve exponential equations algebraically and graphically.

10.g. you define logarithmic functions with base a- also discuss possible values
for the base.

10.h. you define the common logarthimic function and the natural logarithmic
function.

10.i. you discuss the inverse relationship between the logarithmic function and
the exponential function (same base).

10.j. you determine the domain and range of logarithmic functions.

10.k. you produce the graph of a logarithmic function (with various bases)
considering the domain and the range.

10.l. you solve exponential and logarithmic functions algebraically and
graphically.

**11.Solve non- linear systems of equations
Performance Standards**

Competence will be demonstrated:

11.a. by submitting all in-class and take home assignments with passing grades
according to the grading scale in the syllabus.

11.b. by participating actively in class discussions and activities.

Performance will be successful when:

11.a. you solve a nonlinear system of equations algebraically.

11.b. you use graphing calculator to solve non-linear systems of equation.

11.c. you use nonlinear systems of equation to solve applied problems.

**12.Solve systems of linear equations
Performance Standards**

Competence will be demonstrated:

12.a. by submitting all in-class and take home assignments with passing grades
according to the grading scale in the syllabus.

12.b. by participating actively in class discussions and activities.

Performance will be successful when:

12.a. you solve systems of linear equations in three or more variables
algebraically.

12.b. you use the graphing calculator to solve systems of linear equations in
three or more variables.

12.c. you use systems of three equations to solve applied problems.

**13.Perform basic operations with matrices
Performance Standards**

Competence will be demonstrated:

13.a. by submitting all in-class and take home assignments with passing grades
according to the grading scale in the syllabus.

13.b. by participating actively in class discussions and activities.

Performance will be successful when:

13.a. you add matrices.

13.b. you subtract matrices .

13.c. you multiply a matrix by a scaler.

13.d. you multiply matrices when possible.

13.e. you solve application problems using basic operations with matrices.

13.f. you perform basic operations with matrices using the graphing calculator.

**14.Use the inverse of a square matrix
Performance Standards**

Competence will be demonstrated:

14.a. by submitting all in-class and take home assignments with passing grades
according to the grading scale in the syllabus.

14.b. by participating actively in class discussions and activities.

Performance will be successful when:

14.a. you recognize the identity matrix of a square matrix.

14.b. you recognize when two square matrices are inverses of one another.

14.c. you find the inverse of a square matrix, if it exists.

14.d. you use inverses of matrices to solve systems of equations.

14.e. you solve application problems involving matrix inverses.

14.f. you use a graphing calculator to compute matrix inverses.

**15.Solve systems of equations using matrix equations
Performance Standards**

Competence will be demonstrated:

15.a. by submitting all in-class and take home assignments with passing grades
according to the grading scale in the syllabus.

15.b. by participating actively in class discussions and activities.

Performance will be successful when:

15.a. you identify a matrix equation.

15.b. you write matrix equations as a system of linear equations.

15.c. you write a system of linear equations as a matrix equation.

15.d. you find the solution of a system of linear equations by using inverses of
matrices.

15.e. you solve application problems using systems of linear equations and
matrix equations.

**16.Solve systems of linear inequalities
Performance Standards**

Competence will be demonstrated:

16.a. by submitting all in-class and take home assignments with passing grades
according to the grading scale in the syllabus.

16.b. by participating actively in class discussions and activities.

Performance will be successful when:

16.a. you graph linear inequalities algebraically .

16.b. you graph systems of linear inequalities algebraically.

**17.Produce the graph of a conic section
Performance Standards**

Competence will be demonstrated:

17.a. by submitting all in-class and take home assignments with passing grades
according to the grading scale in the syllabus.

17.b. by participating actively in class discussions and activities.

Performance will be successful when:

17.a. you distinguish between the type of conic sections produced when a
quadratic polynomial in two unknowns is graphed.

17.b. you find the center and the semi-major and semi-minor axes given the
polynomial form of the equation of an ellipse .

17.c. you find the center, the axes, and the asymptotes given the polynomial
form of the equation of a hyperbola .

17.d. you find the center, the axis, and the directrix given the polynomial form
of the equation for a parabola.

17.e. you sketch the graph of a conic section given its equation in polynomial
form.

**18.Solve problems involving sequences and series
Performance Standards**

Competence will be demonstrated:

18.a. by submitting all in-class and take home assignments with passing grades
according to the grading scale in the syllabus.

18.b. by participating actively in class discussions and activities.

Performance will be successful when:

18.a. you find terms of sequences given the nth term.

18.b. you find a general term for a sequence.

18.c. you convert between sigma notation and other notation for a series.

18.d. you find the nth term of an arithmetic and geometric sequence.

18.e. you find the common difference of an arithmetic sequence.

18.f. you construct an arithmetic and geometric sequence.

18.g. you find the common ratio of a geometric sequence.

18.h. you find the sum of the first n terms of an arithmetic and geometric
sequence.

18.i. you find the sum of an infinite geometric series, if is exists.

**19.Use the Binomial Theorem
Performance Standards**

Competence will be demonstrated:

19.a. by submitting all in-class and take home assignments with passing grades
according to the grading scale in the syllabus.

19.b. by participating actively in class discussions and activities.

Performance will be successful when:

19.a. you expand a power of a binomial using Pascal's triangle or factorial
notation.

19.b. you find a specific term of binomial expansion.

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