Math 1330 Final Exam Review Covers all material covered in class this semester.

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1 Math 1330 Final Exam Review Covers all material covered in class this semester. 1. Give an equation that could represent each graph. A. Recall: For other types of polynomials: End Behavior An even-degree polynomial s end behavior will be positive and if its leading coefficient is negative. An odd-degree polynomial s end behavior will be positive or if its leading coefficient is negative. if its leading coefficient is if its leading coefficient is Description of the Behavior at Each x-intercept 1. Even Multiplicity: The graph touches the x-axis, but does not cross it (looks like a parabola there).. Odd Multiplicity of 1: The graph crosses the x-axis (looks like a line there). 3. Odd Multiplicity greater than or equal to 3: The graph crosses the x-axis and it looks like a cubic there. B. Math 1330 Final Exam Review 1

2 . Let f ( x) = 7x + 1 and g( x) = x 4, find fi g, its y-intercept and its end behavior. h = fi g y-intercept: end behavior. Degree: Leading Coefficient: 3. Find the inverse of 6x + 4 h ( x) =. x + 3 x + 7x Given f ( x) =. x x 15 A. Find the horizontal asymptotes, if there is one. Recall: Horizontal Asymptotes 1. If deg(n) > deg(d) then there is no horizontal asymptote.. If deg(n) < deg(d) then there is a horizontal asymptote and it is y = 0 (x-axis). 3. If deg(n) = deg(d) then there is a horizontal asymptote and it is y = b a, where a is the leading coefficient of the numerator and b is the leading coefficient of the denominator. B. Find any holes. C. any vertical asymptotes. Math 1330 Final Exam Review

3 Recall: *Parabola: ( y k) = 4 p( x h) or ( x h) = 4 p( y k) If 4p > 0 opens right if y is squared, opens up if x is squared. If 4p < 0 opens left if y is squared, opens down if x is squared. x h + y k = r *Circle: ( ) ( ) ( x h) ( y k) *Horizontal Ellipse: For a > b, + = 1 (bigger number is under x- a b squared) Vertices and Foci are on the horizontal axis. ( x h) ( y k) *Vertical Ellipse: For a > b, + = 1 (bigger number is under y-squared) b a Vertices and Foci are on the vertical axis. ( x h) ( y k) *Horizontal Hyperbola: = 1 (x-term is positive) a b Vertices and Foci are on the horizontal axis. ( y k) ( x h) *Vertical Hyperbola: = 1 (y-term is positive) a b Vertices and Foci are on the vertical axis. 5. Graph y = 16x. Find the: orientation: vertex: focus: directrix: 6. Given y x = 1, find: 16 9 A. Asymptotes. B. Foci rise Recall: y = ± Recall: run c = a + b x y 7. Given + = 1, find: 16 9 A. Vertices. B. Foci. Recall: c = a b Math 1330 Final Exam Review 3

4 8. Write the equation of the circle with center (-5, ) and has radius Write y + y + 8x + 17 = 0 in standard form and find the vertex. 10. Find the x-value(s) of the point(s) of intersection of: f ( x) = x + 8x 5 g( x) = 6x 5 Math 1330 Final Exam Review 4

5 11. Evaluate. π π A. cos sin 4 4 B. 1 cot π 3 4 Recall: RESTRICED DOMAINS QUADRANTS 1 AND 4 π π Inverse sine:,, Inverse cosecant: π π π π,0 0,, Inverse tangent:, QUADRANTS 1 AND Inverse cosine: [ 0,π ], Inverse secant: 1. Evaluate. π, π, π 0, Inverse cotangent: ( 0,π ) 1 A. sin 1 3 B. cos Find sec sin. 11 Math 1330 Final Exam Review 5

6 3π Suppose that π < α < and that tan( α ) =. Find the rest of the trigonometric 7 functions of α. cotα sinα cscα cosα secα 15. Write a sine function of the form y Asin ( Bx) A: Period: π B = with amplitude 5 and the period is. 16. A cosine graph with amplitude 16 has a maximum value of. What is its minimum value? Recall: M m = Amplitude Math 1330 Final Exam Review 6

7 17. Which of these is an equation of one of the asymptotes of the following function? π A. g( x) = sec x Recall: f ( x) = cos( x) A. π x = B. 4 π x = C. x = 3 D. x = π B. h( x) = csc x Recall: A. x = 1 B. x = π C. x = 3 D. x = 18. Find the phase shift for the following function 1 f ( x) = 8cos π x + π Math 1330 Final Exam Review 7

8 19. Sketch the graph of A. f ( x) = 4sin( x). Amplitude: A = Period: π = B Phase Shift: C B = One cycle begins at the phase shift and ends at: C π + B B Any other transformations? Math 1330 Final Exam Review 8

9 B. g( x) = cos(4 x). Amplitude: A = Period: π = B Phase Shift: C B = One cycle begins at the phase shift and ends at: C π + B B Any other transformations? Math 1330 Final Exam Review 9

10 0. Simplify sin x sin x. 1 cos x 1+ cos x A. 0 B. cos x C. sin x D. cot x 1. Simplify 1 (sin x + sin x cos x + cos x). A. (1 sin x cos x) B. sin( x) C. 0 D. sin x. Given sin (y) = 5 7 with 90 o < y < 180 o, find the exact value of sin ( 4 π + y). Recall: sin( A + B) = sin Acos B + cos Asin B Math 1330 Final Exam Review 10

11 3. In triangle ABC, angle C is 90 o, angle B is 55 o and side AB is 0. Find AC. 4. A ramp leading to the freeway overpass is 190 feet long and rises 3 feet. What is the angle of elevation of the ramp to the freeway? 5. Find the area of: A. an equilateral triangle with side lengths 8. 1 Recall: A = absinθ B. triangle XYZ if Y = 90, x = 6 and y = 9. 1 Recall: A = bh Math 1330 Final Exam Review 11

12 π 6. Determine all solutions to sin( 3x ) = 1 on the interval [ 0, ) Solve. sin(x) = -1cosx on [,π ] Recall: sin( x) = sin xcos x 8. ABC is a triangle with AB = 10, BC = 13, and AC = 7. Find cos(a). Note: You are asked to find cos(a) not the measure of angle A. Do not use a calculator. Math 1330 Final Exam Review 1

13 9. In triangle DEF sinx= 3, what are the possible angles of x Given triangle ABC with AB = 5 and BC = 3. The measure of angle A is 30 o. 3 What is the possible measures of angle C? Math 1330 Final Exam Review 13