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# math 116 study guide Math 116

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This 2 page Study Guide was uploaded by Hope Drews on Thursday April 14, 2016. The Study Guide belongs to Math 116 at University of Wisconsin - Milwaukee taught by Chudamani Poudyal in Spring 2016. Since its upload, it has received 16 views. For similar materials see College Algebra in Math at University of Wisconsin - Milwaukee.

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Date Created: 04/14/16

College Algebra Study Guide 1. Solve 3^2x+1=4^3x 2. Consider a function f(x)=5^x a. What are the transformations from the function f(x) to the function g(x)=5^x-2 -25 b. Give the two ordered pairs which lie on the graph of g(x). c. Are there any asymote for the graph of g(x)? d. Sketch the graph of g(x). e. Find the domain and range of g(x) in interval notation. f. Find the x-intercepts of g(x) 3. Solve the following equations: a. Log(3x+2)=log(x+4)+1 b. E^2x-3e^x -40=0 4. Consider the following equation of an ellipse: 5x^2+8y^2+40x-16y+48=0 a. Write the given equation of the ellipse in standard form. b. Compute the following i. Center ii. Vertices iii. Foci iv. End points of major axis v. End points of minor axis c. Sketch the graph of the ellipse. 5. A. Determine the standard form of the parabola with vertex (-4,7) and focus (- 4,-1) B. What is the directrix of the parabola which you got in part A? C. What is the length of the focal diameter? 6. Consider a system of equations: 2x^2+2y^2=50 X+y=2 a. Solve the system algebraically. b. Can you justify your solutions to the system for part a graphically? 7. Given: 11x^2-7y^2+44x-6y-145=0 a. Write the equation of the hyperbola in standard form b. Identify the following and sketch the graph. i. Center ii. Vertices iii. Foci 8. Convert the following general form of the ellipse into the standard form and graph it. 25x^2+16y^2+250x+225=0 i. The center of the ellipse (h,k) ii. Vertices of the ellipse: iii. Major and minor axes: iv. Minor axis end points: v. Foci 9. Find the foci of the hyperbola -9x^2+y^2+54x-117=0 10.Graph the following equations on the same axes and solve the system. X^2+y^2=1 y=1\2(x+2)

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