1. Determine whether the graph below is that of a function by using the vertical line test. a. b.
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1 Math Eam Study Guide Lana (Fall 011) Identify the graph of a function. Use the vertical-line test. 1. Determine whether the graph below is that of a function by using the vertical line test. Determine Even and Odd functions from a graph as well as from an equation.. Determine if the function is even or odd or neither. Use the graph of a function to determine where the function is increasing, decreasing or constant. 3. List the intervals on which the graph of the function is increasing, decreasing or constant.
2 Use the graph to locate local maima and local minima 4. List the values of at which f has a local maimum or a local minimum. What are the maimum and minimum values? Use a graphing utility to approimate local maima and minima and to find increasing or decreasing intervals. 5. Use a graphing utility to graph Find the average rate of change of a function. f () on the interval (-10,10). Approimate the local maima and local minima of the function. Round to decimal places. 6. Let g() 8. Find the average rate of change from = 7 to = 8. Then find an equation of the secant line containing the points 7,g(7) and 8,g(8). Graph and evaluate piecewise-defined functions. 7. Let if 0 f () 1 if 0 if 0 Find: (a) f ( 3) (b) f (0) (c) f (1) 8. The graph of a piecewise-defined function is given. Write a definition for the function that best describes this graph. 9. Graph the piecewise-defined function Find the domain and range. f () 1 if if
3 if 0 1 if Graph the piecewise-defined function g() if 0 < 1 if 3 Find the domain and range. Transformations of functions: vertical and horizontal shifts, compressing, stretching, reflection. 11. Use transformations to sketch the graph of each function without the aid of a calculator. b. f ( ) ( 4) 1 1 g( ) 4 Mathematical modeling: geometric problems, maimizing area, maimizing volume, etc. 1. A rectangle in the first quadrant has one corner on the graph of origin, a third on the positive y-ais, and the fourth on the positive -ais. Epress the area A of the rectangle as a function of. b. What is the domain of A? y 4, another at the c. Graph A A( ) with a calculator. For what value of is A the largest? (Round your answer to two decimal places.) 13. An open bo with a square base is to be made from a square pieces of cardboard 30 inches on a side by cutting out a square from each corner and turning up the sides. Epress the volume V of the bo as a function of the length of the side of the square cut from each corner. b. What is the volume if a 4-inch square is cut out? c. Graph V V ( ) with a calculator. For what value of is V the largest? Draw and interpret scatter diagrams. Distinguish between linear and nonlinear relations. Use a graphing utility to find the line of best fit by linear regression. 14. Use the data from the table to create a scatter diagram on your calculator y Find the equation of the line containing the first and last data point. b. Use a graphing utility to find the line of best fit. Round constants to 3 decimal places.
4 Find the verte, ais of symmetry and intercepts of a quadratic function. Then graph it. 15. Answer the following for the quadratic function f ( ) Does the graph open up or down? b. What is the verte hk, of f? c. What is the ais of symmetry? d. What are the -intercepts? What is the y-intercept? (Write answers as ordered pairs.) Find the maimum or minimum value of a quadratic function by finding the verte. 16. Determine, without graphing, whether the quadratic function maimum value or a minimum value and then find the value. f ( ) has a 17. The function H( ) models the number of individuals whose age is and engage in hunting activities. Use a calculator to answer the following questions. What is the age at which there are the most hunters? (Round down to the nearest whole number.) b. Approimately how many hunters are this age? (Round to the nearest integer as needed.) Identify polynomial functions and their degree. 18. Determine whether each function is a polynomial function. If it is, state the degree. If it is not, tell why not. f ( ) 3 b ( ) 8 g c. h( ) 5 Identify the real zeros of a factored polynomial function and their multiplicity. Determine if the graph of a polynomial touches or crosses the -ais at each -intercept. 19. Form a polynomial with leading coefficient of 1, whose zeros and degree are given. Zeros: 3, multiplicity 1;, multiplicity ; Degree 3. Determine end behavior, intercepts, turning points, domain/range and sketch the graph of a factored polynomial. 0. Analyze the function f ( ) ( 10)( 5) without the aid of a graphing utility. Determine the end behavior of the graph of the function. b. Find the - and y-intercepts of the graph of the function. c. Determine the zeros of the function and their multiplicity. Use this information to determine whether the graph crosses or touches the -ais at each zero. d. Find the domain and range of the function. e. Graph the function without a calculator. Label all intercepts on your graph. 6
5 Find the domain of a rational function. Find the vertical and horizontal asymptotes of a rational function. 1. Find the domain of each rational function. Then find the vertical and horizontal asymptotes. b. h ( ) f( ) Analyze the graph of a rational function: find the domain, intercepts, asymptotes and graph by hand.. Complete steps (a) (g) below for each of the following rational functions then check your results with a graphing calculator. R ( ) 16 R ( ) 6 Factor the numerator and denominator and find the domain. b. Write R in lowest terms. c. Find the -intercepts, if any, and the y-intercept, if it eists. d. Locate the vertical asymptotes. e. Locate the horizontal (or oblique) asymptotes. f. Locate any point discontinuities (holes) in the graph. g. Use the above results to sketch a graph of R by hand. Solve applied problems involving rational functions. 3. The concentration C of a certain drug in a patients blood stream t hours after injection is given t by Ct () 3t 8. Find the horizontal asymptote of C. b. As t increases, what value will C(t) approach? c. Use a graphing utility to determine when the concentration is highest. Round your answer to two decimal places.
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