Precalculus Fall Final Exam REVIEW Evaluate the function at the specified value(s) of the independent variable and simplify.

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1 Precalculus Fall Final Eam EVIEW Model the following situation with a linear equation in slope-intercept form. 4 The gas tank in a truck holds 15 gallons. The truck uses gallon per mile. 7. Evaluate the function at the specified value(s) of the independent variable and simplif. 5 gbg ; gbn g. A publishing compan estimates that the average cost (in dollars) for one cop of a new scenic calendar it plans to produce can be approimated b the function Cbg where is the number of calendars printed. Find the average cost per calendar when the compan prints 0 calendars. 4. Find the domain of the function. f Use a graphing utilit to find an relative minimum or maimum values of the function. f Describe the transformation that occurs in the function. b g b g g 5 7. If f 5 and g 4, find (a) g f 8. Find an equation that represents as a function of. b gb g and (b) b f ggbg. [A] [B] 7 [C] 8 [D] b g that represents as a function of. mb 1 g, b8 1g, b8 1g, b1 8gr [C] mb 1, g, b, 8g, b 1, 1gr mb 1 g, b 1g, b1 1gr [D] l 1,, 8, 1q 9. Find a set of ordered pairs, [A],,,, [B],,, b g b g b g b g. Construct a model of the relation m 6,,, 1, 6, 1, 7, 6r. Determine whether the relation is a function.

2 Precalculus Fall Final Eam EVIEW Evaluate the function at the specified value(s) of the independent variable and simplif. f ; f 9 b g 1. Find the domain of the function. 5 hbg 6 1. Find f g c h b gb g and b f ggb g 4 for f 5 and g If fbg and gbg 5, find b f ggbg. 15. Find the inverse of the function. f 5, 8, 8, 5, 8, 9 b g mb g b g b gr 16. The table shows Christine s best javelin throws each ear. Use a graphing utilit to determine an equation for the line of best fit for the data. Use 0 for Year Distance (m) Find the equation of a quadratic function whose graph opens upward. [A] f b g b g 8 11 [C] fbg 9b 5 9g [B] f 8 9 [D] f Find the graph of the quadratic function. f [A] [B]

3 Precalculus Fall Final Eam EVIEW [C] [D] 19. Sketch the graph of the quadratic function and list an -intercepts. f 0. Write the equation of the quadratic function in standard form and find the verte of the graph. f Upco Manufacturing estimates that its profit P in hundreds of dollars is P 6 1 where is the number of units produced in thousands. How man units must be produced to obtain the maimum profit?. Find the equation of the function graphed below. [A] f [B] f [C] f [D] f. Find a polnomial function that has zeros at 1,, and 1 and matches the graph below.

4 Precalculus Fall Final Eam EVIEW [A] f [B] f [C] f [D] f 4. Factor 8 given that is one of its factors. 5. Find the standard form of the given comple number. 1i 4i 6. Find all the zeros of the function. 4 f Determine the domain of the function. f b g b 1 g 8 6 b gb g 8. Find the horizontal asmptotes, if an, of the graph of f Find the vertical asmptote(s), if an, for f The population of an endangered animal species is given b b g b g t f where 70 is the number of animals currentl in the population and t is the time in ears. The population is decreasing at an annual rate of 17%. What is the estimated number of animals in this population in 5 ears? 1. Sketch the graph of the function. f 1

5 Precalculus Fall Final Eam EVIEW Sketch the graph of the logarithmic function. f log 6 b g b g. Use the properties of logarithms to epand the epression. (Assume all variables are positive.) 6 log 8 4. Solve the eponential equation algebraicall e Find the value of. b g 5. log b g 6. log log Find the value of. 7. 5ln An automobile manufacturer is introducing a new fuel-efficient model and estimates the demand for the car as N = 57,000 lnb6t 7g where N is the estimated number of cars to be sold and t is the number of ears after the car is introduced. When will the demand be 15,000 cars? 9. Find a graph that models an eponential growth function. [A] [B]

6 Precalculus Fall Final Eam EVIEW [C] [D] 40. Earl in the 1900s, an airplane manufacturer was able to increase the time its planes could sta aloft b constantl refining its techniques. Use a graphing utilit to find an eponential equation that best models the data. Assume is the number of ears after 19 and is the time aloft in hours. Years after Time aloft (h) Solve the sstem b the method of substitution. 8 S T 4. Solve the sstem b elimination S T 6 4. Use back-substitution to solve the sstem of linear equations. 7 7 z 5 S T 9 z 5 z Solve the sstem of linear equations using Gaussian elimination. 7 z 6 S T 5 5 z 1 z 45. Determine the order of the matri.

7 Precalculus Fall Final Eam EVIEW Find a matri that is equal to the matri below. [A] [B] [C] [D] Evaluate the epression. 4A 7B A , B Find the inverse of the matri (if it eists) Find the determinant of the matri Find the product, if possible. AB, if A 0 4 1, 1 0 B

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