Chapter 2-4 Review. Find the equation of the following graphs. Then state the domain and range: 1a) 1b) 1c)

Transcription

1 Chapter - Review Find the equation of the following graphs. Then state the domain and range: a) b) c) a) b) c) a) b) c)

2 Find the domain of the following functions. Write your answer in interval notation: a) f(x) = x 7x + x + b) g(x) = a) h(x) = x x x x +x b) p(x) = x x+ A) Determine if the following defines y as a function of x. B) Find the domain and range: a) x + (y ) = b) x + y = 7a) {(, ), (, ), (, ), (, )} 7b) {(, 7), (, ), (, ), (, 9)} Determine if the following functions are even, odd or neither. Show your justification: 8a) f(x) = x 7x 8b) g(x) = x + x 8c) h(x) = x + x 9a) 9b) 9c) Solve the following inequalities. Write your answer in interval notation: a) x + x b) x 7x < 7 Find the equation in standard form and sketch the graph: a) x + y + x y + = b) x + y x + y = Sketch the graph: a) f(x) = x+ + b) g(x) = (x ) + a) h(x) =. x + b) r(x) =.7[[x]]

3 For problems & use the graph of f(x) below: f(x) ) Graph g(x) = f(x ) ) Graph h(x) =. f(x + ) + For the given functions: a) Give the domain and range. b) Give the coordinates of the vertex. c) Give the equation of the axis of symmetry. d) Find the x-intercepts. e) Find the y-intercepts. f) Write the equation in graphing form and sketch the graph. a) f(x) = (x ) b) g(x) = (x + ) + 7) h(x) = x x + 8) f(x) =.x x + Given f(x) = x + x 8, g(x) = x+, & p(x) = x + x, find and simplify: 9a) (g p)() 9b) (f + g)( ) 9c) g(x + ) 9d) f(x ) a) (f + p)(x) b) (p g)(x) c) (f p)(x) d) ( f g )(x) a) f(x+h) f(x) h b) Given the function f, find the following: { g(x+h) g(x) h {.x +, x < x+ +, x < f(x) = x, x < g(x) = x +, x x, x x +, x > a) f( ) b) f() c) The graph of f(x). a) g() b) g( 8) c) The graph of g(x).

4 Identify the function that best fits the data in each graph: a) b) c) a) b) c) Use the graph to the right to find the following: a) The intercepts. b) The intervals where the function is increasing. c) The intervals where the function is decreasing. 7a) The domain and range (in interval notation) 7b) The local extrema. 7c) The absolute extrema. 8a) The intervals where f(x). 8b) The intervals where f(x).

5 Use the graph to the right to find the following: 9a) The intercepts. 9b) The intervals where the function is increasing. 9c) The intervals where the function is decreasing. a) The domain and range (in interval notation) b) The local extrema. c) The absolute extrema. a) The intervals where f(x) >. b) The intervals where f(x) <. Solve the following: ) Suppose a manufacture of a flat screen TV's found that when the unit price is p dollars, the revenue R (in dollars) is R(p) =.p + p. a) At what prices is the revenue zero? (round to the nearest cent) b) For what range of prices will the revenue exceed $,,? (write your answer in interval notation and round to the nearest cent) ) The stopping distance d, (in feet), on dry, level concrete for a particular truck and the speed of a truck, v (in mph), is given by d(t) =.v +.7v. a) If a truck is traveling mph, how many feet are needed for it to stop? (round to the nearest feet) b) If there is an accident 7 feet ahead, what is the maximum speed the truck could be traveling and still be able to stop in time? (round to the nearest mph) ) A Ferris wheel has a maximum height of feet with a wheel diameter of 8 feet. Find an equation for the wheel if the center of the wheel is on the y-axis and y represents the height above the ground. Write the answer is standard form. ) In, the population of Austin was 7 thousand. By, the the population of Austin was 9 thousand. Find and interpret the average rate of change (round to one decimal place).

6 Solve the following: ) The average price per gallon of milk for the year is given below: a) Find the average rate of change of the cost of gallon of milk between January and May of. Interpret the result. b) Find the average rate of change of the cost of gallon of milk between April and August of. Interpret the result. 7) A cell phone company offers a monthly cell phone plan for $9.99. It includes 9 anytime minutes plus $. per minute for additional minutes. The following is used to compute the monthly cost for a subscriber, where x is the number of minutes used. { 9.99, if x 9 C(x) =.x., if x > 9 a) Find C(8) and C(9). Round to the nearest cent. b) The cell phone company offers a second plan that cost $8.99 per month for the first minutes. How many minutes in a month must a customer use for this plan to be cheaper than the other plan? 8) A ball is thrown vertically upward with an initial velocity of 9 feet per second. The distance s (in feet) of the ball from the ground after t seconds is s(t) = 9t t, a) At what time t will the ball strike the ground? b) For what time t is the ball more than feet above the ground? (round your answer to two decimal places.) c) What is the maximum height the ball will reach? At what time will this occur?

7 Solve the following: 9) A trucking company transports goods between two cities that are 9 miles apart. The company charges, for each pound, $. per mile for the first miles, $. per mile for the next miles, $.7 per mile for the next miles, and no charge for the remaining miles. a) Graph the relationship between the cost of transportation in dollars C(x) and mileage x over the entire 9-mile route. b) Find the cost as a function of mileage for hauls between and miles from the first city. c) Find the cost as a function of mileage for hauls between and 8 miles from the first city. ) If a basketball player shoots a foul shot, releasing the ball at a certain angle from a position feet above the floor, then the path of the ball can be modeled by the quadratic function, h(x) = 8.x v +.8x +, where h is the height of the ball above the floor, x is the forward distance of the ball in front of the foul line, and v is the initial velocity with which the ball is shot in feet per second. Suppose a player shoots a ball with an initial velocity of feet per second. a) Determine the height of the ball after it has traveled feet in front of the foul line (round to two decimal places). b) Find the maximum height the ball will reach and the distance the ball is forward of the foul line when it reaches that height. (round to two decimal places). c) The center of the hoop is feet above the floor and feet in front of the foul line. Will the ball go through the hoop? If not, what is the initial velocity needed for the ball to go through the hoop? (round to two decimal places).

8 Answers: a) f(x) = x + ; D: [, ), R: (, ] b) f(x) = x ; D: (, ), R: [, ) c) f(x) = (x + ) + ; D: (, ), R: (, ) a) f(x) = (x + ) ; D: (, ), R: [, ) b) f(x) = x+ c) f(x) = x ; D: (, ), R: (, ) + ; D: (, ) U (, ), R: (, ) U (, ) a) (x + ) + (y ) = 9; D: [, ], R: [, ] b) f(x) = x ; D: (, ), R: (, ) c) (x ) + (y + ) = ; D: [, ], R: [, ] a) (, ) b) (, ) U (, ) U (, ) a) (, ) U (, ] b) [, ] a) Not a function; D: [, ], R: [, 7] b) A function; D: (, ), R: (, ] 7a) A function; D: {,,, }, R: {,, } 7b) Not a function; D: {,, }, R: {,, 7, 9} 8a) Even since f( x) = f(x) 8b) Neither since g( x) g(x) & g( x) g(x) 8c) Odd since h( x) = h(x) 9a) Even since it is symmetric with respect to the y-axis 9b) Neither since it is not symmetric with respect to the y-axis or the origin. 9c) Odd since it is symmetric with respect to the origin. a) [, ] b) (, 9) U ( 8, ) a) (x + ) + (y ) = 9 b) (x ) + (y + ) =

9 a) b) a) b) ) )

10 a) Domain: (, ) b) Domain: (, ) Range: [, ) Range: (, ] Vertex: (, ) Vertex: (, ) Axis of Symmetry: x = Axis of Symmetry: x = x-intercepts: (, ) & (7, ) x-intercepts: (, ) & (, ) y-intercept: (, ) y-intercept: (, ) ) Domain: (, ) 8) Domain: (, ) Range: [, ) Range: (, 7] Vertex: (, ) Vertex: (, 7) Axis of Symmetry: x = Axis of Symmetry: x = x-intercepts: None x-intercepts: (, ) & ( +, ) y-intercept: (, ) y-intercept: (, )

11 9a) 9b) 9c) x+ 9d) 7x a) x + 8x 8 x b) x + x x+ c) x + x x + d) x b) x+h+ + x+ c) c) x +x 8 x+ a) x + h + a) b) a) 7 b) a) f(x) = x b) f(x) = x b) f(x) = x c) f(x) = x c) f(x) = x a) f(x) = x a) x-ints: (, ) & (, ); y-int: (,.) b) (, ) U (, ) c) [, ) U (, ) U (,.) 7a) D: [,.); R: [, ] 7b) Local minima: (, ), (, ) Local maxima: (, ), (, ) 7c) Absolute maximum of at x =. Absolute minimum of at x =. 8a) [, ] U [,.) 8b) [, ] 9a) x-ints: (.7, ), (, ), (, ), (, ); y-int: (, ) 9b) (, ) U (, ) 9c) (, ) U (, ) a) D: (, ); R: [, ) b) Local minima: (, ), (, ) Local maxima: (,.) c) Absolute maximum: None Absolute minimum of at x =. a) (,.7) U (, ) U (, ) b) (.7, ) U (, ) a) The prices are $ & $. b) ($.,.9) a) feet b) 9 mph ) x + (y ) = ) Austin's population was increasing by. thousand per year.

12 a) The cost of a gallon of milk was increasing by.7 per month. b) The cost of a gallon of milk was decreasing by. per month. 7a) C(8) = $9.99; C(9) = $7.79 7b) The customer must use 9 or more minutes per month. 8a) seconds. 8b) Between. and.78 seconds. 8c) At t = seconds, it will reach a maximum height of feet. 9a) $9 $8 $7 $ $ $ $ $ $ $ b) C(x) = +.x 9c) c(x) = +.7x a). feet b) The maximum height will be.8 feet when the ball is 8. feet from the foul line. c) No, the initial velocity needs to be.7 ft/sec.