# MAT-197 Objectives

## MAT-197 Precalculus

Topics include functions and their graphs, polynomial functions, rational and radical functions, exponential and logarithmic functions, elements of trigonometry and trigonometric functions, analytic geometry, and sequence and series notation. This course meets General Education "Quantitative Thought" Requirement 5.4 credits Prerequisite: Grade of C or better in College Algebra-STEM (MAT194) or placement.

### Instructional Objectives

1. Construct a rectangular coordinate system and interpret it as a representation of ordered pairs of real numbers.
2. Given an equation in algebraic form, construct a table of solution pairs (x,y) and sketch a representative graph.
3. Define, identify and use appropriate notation for each of the following: function, domain, range, independent variable, dependent variable.
4. Use algebraic, numeric and graphic representations of functions to model and solve problems.
5. Define, compute and interpret the slope of a line.
6. Express linear functions in point-slope, slope-intercept, numeric and graphic form: use linear functions to model and solve problems.
7. Define and identify: parallel and perpendicular lines increasing and decreasing functions
8. Define, identify and use appropriate notation for the inverse of a function: express the inverse of a function in algebraic, numeric and graphic form.
9. Given a polynomial or power function of even or odd degree (n\$2), specify its degree, possible zeroes, real and complex roots, turning points, end behavior and orientation of its graph.
10. Use polynomial and power functions to model and solve problems.
11. Find the real roots of a polynomial equation by algebraic or numeric/graphic methods.
12. Given two functions f(x) and g(x), find their sum, difference, product and quotient.
13. Given two functions f(x) and g(x), find the composite functions f(g(x)) and g(f(x)).
14. Given a function f(x), describe the function which will produce a horizontal or vertical translation, stretch, shrink or reflection of the original curve: sketch the resulting function.
15. Sketch a representative graph of the rational function f(x)/g(x) by determining its x and y-intercepts, vertical asymptotes and end behavior.
16. State the general form of the exponential function and sketch its graph.
17. Use the exponential function to model and solve problems involving growth and decay.
18. State the general form of the logarithmic function and sketch its graph.
19. Use logarithmic functions to model and solve problems.
20. State and apply the basic properties of logarithms.
21. State and apply the fundamental logarithmic-exponential identities.
22. Solve exponential and logarithmic equations.
23. *Approximate ex and ln(1+x) with polynomial expansions.
24. Define the six trigonometric ratios in terms of opposite and adjacent sides and the hypotenuse of a right triangle.
25. Find the exact value (or state if it is undefined) of a trigonometric ratio of a special (45E, 30E, 60E) or quadrantal angle.
26. Use a calculator to find the value of a trigonometric ratio of an acute angle given in degree measure.
27. Given the value of a trigonometric ratio of an acute angle, use a calculator to find the angle.
28. Solve a right triangle, given one angle and one side, or two sides: solve verbal problems involving right triangles.
29. Define the trigonometric functions of an angle in standard position in the coordinate system in terms of a point (x,y) and a radius r.
30. Express the measure of an angle in degrees, radians and revolutions.
31. Given any angle (positive or negative) in degree or radian measure, find the least positive coterminal angle and the reference angle.
32. Given an angle (positive or negative) in standard position in degree or radian measure, use a calculator to find the value of a specific trigonometric function.
33. Use a calculator to find all angles between 0E and 360E or 0 and 2π radians having a given trigonometric function value.
34. Sketch the graphs of the six trigonometric functions.
35. State the amplitude, period, phase shift and displacement of a function of the form y = A@sin(Bx + C) + D and sketch its graph.
36. Use trigonometric functions to model and solve problems involving periodic phenomena.
37. State the reciprocal, ratio, and Pythagorean identities and use them to rewrite expressions and solve equations.
38. State the sum, difference, double angle and half angle identities and use them to rewrite expressions and solve equations.
39. State the range of principal values and sketch the graph of the inverse sine, cosine and tangent.
40. * Use the laws of sines and cosines to solve triangles, given two angles and one side, two sides and one angle, or three sides.
41. * Use the laws of sines and cosines to model and solve problems involving triangles.
42. * Approximate sin(x) and cos(x) with polynomial expansions.
43. * Change the form of a complex number (real, pure imaginary or imaginary) from rectangular form to polar form and from polar form to rectangular form.
44. *Use De Moivre's theorem to find powers or roots of complex numbers.
45. * Construct a polar coordinate system and interpret the coordinates (r,Θ) for individual points in the real number plane.
46. * Change coordinates from rectangular form to polar form and from polar form to rectangular form.
47. * Sketch the graph of an equation of the form r = f(Θ) in polar coordinates.
48. * For each of the conic sections (circle, ellipse, hyperbola, parabola), state a verbal definition of the curve, write its equation in standard form and sketch its graph.
49. *Define, identify, give examples and use appropriate notation for each of the following: sequence, term of a sequence and sum of terms of a sequence.

* = optional topic