MAC 1 Review for Eam Name Determine whether the relation represents a function. If it is a function, state the domain and range. 1) {(-3, ), (-, ), (0, 1), (, ), (, 17)} ) {(19, -), (3, -3), (3, 0), (1, 3), (8, )} Find the value for the function. 3) Find f(-) when f() = 3-3 -. ) Find -f() when f() = - 3 +. Find the domain of the function. - ) h() = 3-16 6) f() = 13 - For the given functions f and g, find the requested function and state its domain. 7) f() = ; g() = - 7 Find f g. Solve the problem. 8) Find (f - g)() when f() = -3 + and g() = + 6. Find and simplif the difference quotient of f, 9) f() = + 7 + 8 f( + h) - f(), h 0, for the function. h Determine whether the graph is that of a function. If it is, use the graph to find its domain and range, the intercepts, if an, and an smmetr with respect to the -ais, the -ais, or the origin. ) 1-3 3-1 1
The graph of a function f is given. Use the graph to answer the question. 11) Is f(6) positive or negative? - - 1) For what numbers is f() < 0? - - The graph of a function is given. Decide whether it is even, odd, or neither. 13) 8 6 - -8-6 - - - 6 8 - -6-8 - A) even B) odd C) neither
1) 3 1-1 - -3 - - A) even B) odd C) neither 1) 3 1-1 - -3 - - A) even B) odd C) neither Determine algebraicall whether the function is even, odd, or neither. -3 16) f() = 3 + A) even B) odd C) neither 3
Use the graph to find the intervals on which it is increasing, decreasing, or constant. 17) The graph of a function f is given. Use the graph to answer the question. 18) Find the numbers, if an, at which f has a local minimum. What are the local minima? - Solve the problem. 19) The height s of a ball (in feet) thrown with an initial velocit of 70 feet per second from an initial height of 3 feet is given as a function of time t (in seconds) b s(t) = -16t + 70t + 3. What is the maimum height? Round to the nearest hundredth, if necessar.
Find the average rate of change for the function between the given values. 0) f() = 3 + - 8-7; from 0 to Find an equation of the secant line containing (1, f(1)) and (, f()). 1) f() = 3 - Graph the function. - + if < 0 ) f() = + 3 if 0 - Graph the function and evaluate at the indicated values of. Identif the domain and the range and find the intercepts if an. + 3 if -8 < 3) f() = -9 if = - + 7 if > f(-8) = ; f(0) = ; f() = ; f( ) = ; f(6) = -intercept: Domain: ; -intercepts: ; Range: - - -
The graph of a piecewise-defined function is given. Write a definition for the function. ) (0, ) (3, ) (-3, 0) - - Solve the problem. ) An electric compan has the following rate schedule for electricit usage in single-famil residences: Monthl service charge $.93 Per kilowatt service charge 1st 300 kilowatts Over 300 kilowatts $0.1189/kW $0.1331/kW What is the charge for using 300 kilowatts in one month? What is the charge for using 37 kilowatts in one month? Construct a function that gives the monthl charge C for kilowatts of electricit. Answer the question. 6) How can the graph of f() = 1 ( + ) - be obtained from the graph of =? Write an equation for a function that has a graph with the given characteristics. 7) The shape of = is shifted units to the left. Then the graph is shifted 7 units upward. 8) The shape of = is verticall stretched b a factor of 3, and the resulting graph is reflected across the -ais. 6
9) Find the function that is finall graphed after the following transformations are applied to the graph of =. 1) Shift left 3 units ) Stretched b a factor of 3) Reflect about the -ais ) Shift up units Graph the function b starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. 30) f() = - - 3 Basic function = f() = - - - - 31) f() = - + Basic function = f() = - + - - 7
Graph the function b starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. Find the and -intercepts if an and use the graph to find the domain and the range of the function. 3) f() = - - 6 Basic function = f() = - - 6 -intercept: -intercept: Domain: ; Range: - - - - 8
33) f() = 3( + 1) - 3 Basic Function = f() = 3 +1-3 -intercept(s): -intercept: Domain: ; Range: - - - - 9
Graph the function b starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. Find the and -intercepts if an ; then, use the graph to find the domain and the range of the function. 3) f() = + 6 - Basic function = f() = + 6 - -intercept(s): -intercept: Domain: ; Range: - - - - A graph of = f() follows. No formula for f is given. Make a hand-drawn graph of the equation. 3) = - 1 f() (0, 0) (-6, 0) (6, 0) (-3, -) (3, -)
Solve the problem. 36) A bo with an open top is to be constructed from a rectangular piece of cardboard with dimensions 1 inches b 9 inches b cutting out equal squares of side at each corner and then folding up the sides as in the figure. Epress the volume V of the bo as a function of. 9 1 37) A farmer has 0 ards of fencing to enclose a rectangular garden. Epress the area A of the rectangle as a function of the width of the rectangle. What is the domain of A? 11
Answer Ke Testname: P.011 1) function domain: {-3, -, 0,, } range: {,, 1, 17} ) not a function 3) 3 + 3 - ) - + 3 - ) { -, 0, } 6) { 13} 7) ( f g )() = - 7 ; { 0, 7 } 8) -6 9) + h + 7 ) function domain: { } range: { -1 1} intercepts: (, 0), (0, 0), (, 0) smmetr: origin 11) negative 1) (-3, 3.) 13) C 1) B 1) A 16) B 17) Decreasing on (-3, -) and (, ); increasing on (-1, 1); constant on (-, -1) and (1, ) 18) f has a local minimum at = and ; the local minimum is -1 19) 79.6 ft 0) - 1) = 6-6 ) (0, 3) (0, ) - - 1
Answer Ke Testname: P.011 3) f(-8) = - ; f(0) = 3 ; f() =-9 ; f( ) = ; f(6) = 1 -intercept:(0,3); -intercepts: (-3,0) and (7,0) Domain:[-8, ); Range: (-,7) (, 7) (, 3) - - (-8, -) - - (, -9) ) f() = + if -3 0 3 3 if 0 < 3 ) $39.70 $9.69 C() =.93 + 0.1189-0.66 + 0.1331 if 0 300 if > 300 6) Shift it horizontall units to the left. Shrink it verticall b a factor of 1. Shift it units down. 7) f() = + + 7 8) f() = -3 9) = -(+3) + 30) Ke points of basic function: (0, 0), (1, 1), (, ) ---> (, -3), (6, -), (9, -1) (corresponding points on f()) - - - - 13
Answer Ke Testname: P.011 31) Ke points of basic function: (0, 0), (1, 1), (, ) --> (0, ), (-1, 3), (-, ) (corresponding points of f()) Note:Final graph should be the graph of = - shifted upward units. - - 3) Ke points of basic function: (0, 0), (1, 1), (, ) ---> (, -6), (6, -), (9, -) (corresponding points on f()) -intercept: (1, 0); No -intercept; Domain [, ); Range: [-6, ) - - - - 33) Ke points of basic function: (-1, 1), (0, 0), (1, 1) --->(-, 0), (-1, -3), (0, 0) (corresponding points of f() -intercepts: (-, 0), (0, 0) ; -intercept: (0, 0) - - - - 1
Answer Ke Testname: P.011 3) Ke points of = : (-1, 1), (0, 0), (1, 1) Corresponding points of f() (-7, -), (-6, -), (-, -) -intercepts: (-11, 0), (-1, 0) ; -intercept: (0, 1) Domain: All Reals ; Range: [-, ) -0-1 - - 1 0 - - 3) (-3, ) (3, ) (-6, 0) (0, 0) (6, 0) 36) V() = (1 - )(9 - ) 37) A() = - + 600; { 0 < < 600} 1