Math 112 Spring 2016 Midterm 2 Review Problems Page 1

Transcription

1 Math Spring Midterm Review Problems Page. Solve the inequality. The solution is: x x,,,,,, (E) None of these. Which one of these equations represents y as a function of x? x y xy x y x y (E) y x 7

2 Math Spring Midterm Review Problems Page. Which one of the following graphs DOES NOT represent a function?

3 Math Spring Midterm Review Problems Page. Which one of the tables below represents y as a function of x? x y x y x y x y (E) x y. Given f r r r, evaluate t f. t t 7 t t t 7 t t (E) t. Which one of the following points lies on the graph of the equation y x?,,,,

4 Math Spring Midterm Review Problems Page 7. For f x x 9x, find and simplify f ( x h) f ( x). h xh h 8x 9h 8 h h h 8x 8 h x h 9 x h (E) x 9 8. Determine the domain of x x x,, x,, x, (E) x, x g. x x 9. Determine the zero(s) of x x only x,, and x and only x only (E) x and only x r. x x only

5 Math Spring Midterm Review Problems Page. Determine the domain of hx 7x., 7, 7,, (E), 7 7. Determine the domain of f x denominator separately first.) x x. (Hint: Determine the domain of the numerator and,,,, (E) None of these. Which one of the following has a domain of all real numbers except x? y x y x y x x y (E) x 8 x y x

6 Math Spring Midterm Review Problems Page. The graph of gx g. y is shown below. Use the graph to determine the domain and range of g x Domain: (, ) Range: [, ) Domain: [., ) Range: [, ) Domain: [, ) Range: [., ) Domain: [., ) Range: [., ) (E) Domain: [, ) Range: (, ) - -. The graph of y f x is shown below. Use the graph to determine the value of f f x (E)

7 Math Spring Midterm Review Problems Page 7. Identify the open interval(s) where the graph of T x y is decreasing., and, only, only, only, and, (E), only only. Identify the open interval(s) where the graph of T x y is positive., only, and, only, only, and, (E), and, only only

8 Math Spring Midterm Review Problems Page 8 7. Given that Lx y is an odd function, complete the table of values: x L x The missing values, from left to right, are:,,,,,,,, (E) None of these 8. Given that Lx y is an even function, complete the table of values: x L x The missing values, from left to right, are:,,,,,,,, (E) None of these

9 Math Spring Midterm Review Problems Page 9 9. Determine which one of the following graphs represents an even function

10 Math Spring Midterm Review Problems Page. Determine which one of the following graphs represents an odd function

11 Math Spring Midterm Review Problems Page. Determine which one of the following represents an odd function. g x x. f x x R m m m ht t t (E) F x x. Evaluate g given that: g x x x for x x for x and (E) None of these. Determine the domain and range of x Domain:, x for x f. x for x, Domain:, Range:, Range:, Domain:, Range:, Domain:,, Range:,,. Determine the range of the function given by g x x x x x (,] (,] (,) (,) (E) (, )

12 Math Spring Midterm Review Problems Page. Which one of the following is the graph of the function x x if x f? if x

13 Math Spring Midterm Review Problems Page. Determine the rule that defines the piecewise-defined function graphed below x x if x f x f x if x x x if x if x x x if x f x f x if x x x if x if x 7. If, is a point on the graph of y rx on y? the graph of rx, which one of the following points MUST be,,,, (E),

14 Math Spring Midterm Review Problems Page 8. Which one of the following transforms the graph of f x and a horizontal stretch? y f x y f y f x x (E) y f x y f x y with a vertical compression 9. Suppose gx ( 7, 7] (, ] (, ] (, ] (E) (, 8] y has a domain of, ] (. What is the domain of gx y?. Suppose the graph of y x is transformed into following describes the transformations performed? Horizontal compression, reflect over the x-axis, shift right Vertical compression, reflect over the x-axis, shift left Vertical compression, reflect over the y-axis, shift left Vertical compression, reflect over the x-axis, shift right (E) Horizontal expansion, reflect over the y-axis, shift left y x. Which one of the 7

15 Math Spring Midterm Review Problems Page. Consider the table of values for the function hx y given below. x h x 8 Which one of the following tables of values represents hx y? (E) x 8 x h x 8 x h 8 x 8 x h x x h x. x h

16 Math Spring Midterm Review Problems Page. Consider the graph of f x y given below, Which one of the following represents the graph of - x y f?

17 Math Spring Midterm Review Problems Page 7. The graph of y x can be obtained from the graph of y x by Shifting up units and reflecting over the x-axis. Shifting right units and reflecting over the x-axis. Shifting left units and reflecting over the y-axis. Shifting right units and reflecting over the y-axis. (E) Shifting left units and reflecting over the x-axis. Let f x and g x x x f g. Evaluate and simplify x x x x x x x x x (E) None of these. Use these functions to answer the next two questions... Evaluate and simplify gx x x x x x (E) x x f. x. Consider the functions S x x and T x. Find T S.

18 Math Spring Midterm Review Problems Page 8 (E) Consider the functions x answer the next three questions. 7. Evaluate g f. (E) Undefined 8. Evaluate f (E) g. 9. Evaluate g f. f and x x g represented in the tables below. Use these tables to f x x g x (E) M N. Determine the domain of x if M x x and x x x N.

19 Math Spring Midterm Review Problems Page 9 (, ) (,) (,) (, ) (, ) (,) (, ) (,) (, ) (, ) (,) (,) (, ) (E) (, ) (,) (, ) x. Determine the domain of R T x if R x and x x T.,,,,,,,, (E),,. Determine functions f x and g x so that gx following could NOT be choices for f x x and g x x f x and g x x x x x f x and gx x f x and g x x f x and x g? f. Which one of the x. Suppose h x x, where hx f gx. If f x x following is g x?, which one of the g x g x g x x g x x (E) g x x Use the graphs of the functions questions. y M x and Nx y given below to answer the following

20 Math Spring Midterm Review Problems Page Determine the domain of N x M x N x M.,,,, (E),, M N. Determine the domain of x.,,,, (E),,. Determine a formula for the inverse function for x x 7 g. g x x 7 g x x 7 x 7 g x g x x 7 (E) g x x 7 7. Determine a formula for the inverse function for x x h. x

21 Math Spring Midterm Review Problems Page x x h x h x x x h x h x x x x x (E) None of these 8. Use the graph of f x y f x. y given below to determine the RANGE of the inverse function ,,,, (E) None of these 9. Use the graph of f x y f x. y given below to determine the graph of the inverse function

22 Math Spring Midterm Review Problems Page The function R x is described by the set of ordered pairs below

23 Math Spring Midterm Review Problems Page x R x 9 8 Which one of the following tables describes x R? (E) R x 9 8 x x x R 9 8 x x R R 9 8 x x 9 8 x x R 9 8. If f x is a one-to-one function and f 7 y f x?, what point MUST be on the graph of

24 Math Spring Midterm Review Problems Page, 7, 7, 7 7, (E), 7. The cost (in dollars) of introducing a recycling program to p% of the population in a particular town can be modeled by:, p C p p Determine the percent of the population the town can put on the recycling program if the budget for the program is $,. Round your answer to the nearest.% 9.% 9.% 87.8% 8.% (E) 79.9%. The cost (in dollars) of introducing a recycling program to p% of the population in a particular town can be modeled by:, p C p p Interpret the meaning of,. C. For a cost of $,, one can expect.% of the population to be put on the program. For a cost of $,, one can expect, people to be put on the program. For a cost of $., one can expect % of the population to be put on the program. For a cost of $,, one can expect, people to be put on the program. Consider the functions x answer the next two questions. f and x g represented in the tables below. Use these tables to

25 Math Spring Midterm Review Problems Page x f x x g x 7. Evaluate (E) f.. Evaluate g f (E) 7.. Consider the graph of Cx y given below.

26 Math Spring Midterm Review Problems Page What is the value of C?.. 7 (E) 7. If P x x 8, evaluate P. 7 8 (E) None of these 8. Determine g x for g x Ax, where A is a constant. x x Ax g x g x g x A x x g x A x x A (E) None of these 9. Determine whether x 8 x f has a maximum or minimum and then determine the maximum or minimum value.

27 Math Spring Midterm Review Problems Page 7 Max = Min = Min = 8 Max = (E) Max = 8. Consider the function f x x 8 9 TRUE?. Which one of the following statements is The graph opens up. The y-coordinate of the vertex is 9. The graph opens down. The graph has a minimum at the vertex.. Determine the formula for the quadratic function in standard form for the parabola graphed below y x y x y x y x (E) y x. Determine the formula for the quadratic function in standard form that fits the data exactly

28 Math Spring Midterm Review Problems Page 8 H ( t) ( t ) H ( t) ( t ) H ( t) ( t ) 7 8 H ( t) ( t 7) 9 (E) None of these t H t Determine the x-intercepts of f x x x. The largest x-intercept is:,, 7,, 7 (E) None of these. Determine the vertex for the quadratic function x x 8x g.,,,, (E),. Determine a possible formula for the quadratic function that passes through the points,,, and,. y x x y x x y x x y x x (E) y x x. Determine a possible formula for the quadratic function that has a vertex at, passes through the point, 7., and

29 Math Spring Midterm Review Problems Page y x y x y x 7 9 y x (E) y x 7. A mathematical model for the profit, P, in thousands of dollars, that a company makes in one year from producing x units of its product is: P x x x 89, 7. What is the maximum profit the company can make? $, $, $7, $, (E) $, 8. A woman is shooting a basketball toward a basketball hoop. The starting height of the ball is. feet. The path of the basketball is parabolic in shape, and the ball reaches its maximum height of. feet when the ball is feet from the player. The ball hits the front of the rim, which is feet high. Determine the horizontal distance from the shooter to the rim. The distance is: Less than feet Between and feet Between and feet Between and feet (E) More than feet 9. A homeowner wants to fence in a rectangular garden next to a very long stream. Since the garden will border the stream, that side of the garden will not need fencing. What is the largest area that can be enclosed with feet of fencing?, sq ft, sq ft 8, sq ft, sq ft (E) None of these 7. A horticulturist has determined that the number of inches a young redwood tree grows in one year is a function of the annual rainfall, r (in inches), given by

30 Math Spring Midterm Review Problems Page r.r r g What is the maximum number of inches a young redwood can grow in a year? The maximum number of inches is: less than between.9 and. between. and. between. and. (E) between.7 and. 7. When an apple orchard owner plants trees on an acre of ground, he gets an average yield of apples per tree per year. For each additional tree planted per acre, the annual yield per tree drops by apples. Calculate the number of trees that should be planted per acre to produce the maximum crop of apples and use that value to determine the maximum yield? The maximum yield is: 7, apples, apples 97, apples 98, apples (E), apples Bob s high school is performing a musical. If each ticket is priced at $9. then tickets will be sold. For each $. increase in price, fewer tickets will be sold. Use this information to answer the next two questions. 7. Determine the price that should be charged for each ticket to maximize the revenue. (Hint: Revenue is quantity times price.) Less than $9. Between $9. and $9.8 Between $9.8 and $. Between $. and $. (E) More than $. 7. Determine the maximum possible revenue from the musical ticket sales. More than $ Between $ and $ Between $9 and $ Between $8 and $9 (E) Less than $8

31 Math Spring Midterm Review Problems Page A company has determined that the demand function for a dining room table is given by p x where p is the price per table and x is the number of tables sold. The fixed cost of producing a line of dining room tables is $, and each table costs $ to make. Use this information to answer the next three questions. 7. Determine a simplified formula for the revenue function. (Hint: Revenue is quantity times price.) Rx x Rx x Rx x x Rx x (E) Rx x x 7. Determine the quantity that should be manufactured to maximize revenue. The quantity is: Less than 9 tables Between 9 and tables Between and tables Between and tables (E) More than tables 7. Determine the quantity that should be manufactured to maximize profit. The quantity is: Less than 9 tables Between 9 and tables Between and tables Between and tables (E) More than tables

32 Math Spring Midterm Review Problems Page Spring Midterm Study Guide Answers Question Answer Question Answer B 9 C E A B B D C E D D C 7 C E 8 E C 9 A 7 B A 8 A C 9 C D A C D B A A A E E 7 B C 8 C C 9 A 7 D C 8 D D 9 E C B A E D A C A B E 7 D A 8 E A 9 B 7 B B 8 D E 9 B A 7 C E 7 D B 7 B E 7 E E 7 C 7 D 7 D 8 B 7 B