Module C Exam Review Concepts

Module C Exam Review Concepts
To study for your exam, review the following problems and concepts from your homework and calculator
assignments. Then try the sample problems. The questions on the exam will be similar, but not identical.

Symmetry and Transformations
1. Determine if a function is symmetric about the y-axis or the origin. Determine if a relation is
symmetric about the x-axis (Remember that functions can’t have x-axis symmetry because they
would fail the vertical line test ). Review pg. 506 # 2,5; pg.509 # 2,3.

2. Translate graphs by shifting up, down, left, or right.. Review pg. 507-508 # 25,27; pg. 509-510 #
7,9.

Polynomial Functions

3. Determine if a function is polynomial. Review the definition on page 471. Remember that the
exponents of terms can not be negative or fractional; they must be positive whole numbers. Also
remember that a constant function is a polynomial function of the form

4. Identify the leading coefficient and degree of a polynomial function. Recognize that a polynomial
function of degree 1 is a linear function , and a polynomial function of degree 2 is a quadratic
function. Review pg. 506 # 1.

5. Use the procedure outlined in the TI-83 handout to find all of the zeros of a polynomial function.
You will need to be able to used long division or synthetic division . Synthetic division is reviewed in
the web lesson and starting on page 515 . For more practice try the problems on pg. 554 # 37, 39,
41.

6. Graph polynomial functions. Use the procedure outlined in the TI-83 handout on graphing
polynomial functions. This entails finding x-and y- intercepts and points in between.

Rational Functions

7. Find the domain of a rational function. Review pg.507 # 13,16.

8. Find the x-intercepts of a rational function. The x-intercepts may be found by setting the numerator
of the rational function equal to zero and solving for x .
For example, to find the x-intercepts of the function

Solve the equation . We find that x = -1/2 and x = 3 are solutions. Therefore the
x-intercepts of the function are (-1/2,0) and (3,0).

9. find the y-intercepts of a rational function. To do so, evaluate f(0). For the example above,
. So the y-intecept is (0,-1/2).

10. Find all the asymptotes of a rational function. You need to use long division to find oblique
asymptotes. Long division is reviewed on pg. 514. Review pg. 507 # 14,17,23.

11. Graph Rational functions. Use the procedure outlined in the TI-83 handout on graphing polynomial
functions.

Matrices and Applications
12. Find the determinant of a 2 x 2 Matrix. Review pg. 686 # 2.
13. Solve a 2 x 2 system of equations using Cramer’ s rule . Review pg. 687 # 16.
14. Use the Gauss –Jordan method to solve a three variable system of equations. Be able to row reduce
a matrix by hand, showing all of your steps . Review pg. 725 #18.
15. Solve word problems using matrices. Review the homework problems from the handout on
Applications of Matrices.