1) Find the domain and range of the relation. Use interval notation where appropriate. 5 ( 41 0) ( 01 - 2 ) ( 0 1 2 ) (5 1 Domam : 741 - 210, 53 2 Range : 8 - 21 01 213 7 2) Is the graph below the graph of a function? Yes or No 0 12 yes - 4 -4 .3) Find the domain of the following two functions. Write the answers in interval notation. a. ) m (x ) = - x - 1 x + 8 X+8 =0 8 X=-8 -8 ( - P 1 - 8 ) ( - 81 8 ) b. ) g ( y ) = Vy - 4 - 420 41 = 4 4 4) a.) Use the graph to estimate the value of f(-4). F ( -4) 2 2 2 34 b.) Use the graph to estimate the real values of x for which f (x) = 0. 1-3 -2 2 3 4 5 X = 1, 15) Find the x- and y-intercepts of the function. g(x) = -4x - 14 X-Intercept: ~Xx Y-Intercept: - 14 X - 3 6) When f (x) = x + 2 and g(x) = 4x2+4x, find (8 - f)(x) (g - f ) (2 ) : 9 ( x ) - f( x ) = Lex + 4 x = X +2 1 = 4x + 3 x4/2 - 1 7) If f ( x) = 14x + 7 and g(x) = x2 - 2x, find _ (x). ( f / g ) ( x ) = 14 x+ 7 2 - 2X 8) Given: f (x) = x2 - 4x + 1, g(x) =6x a.) Find: (f g) (x) ( fog ) (x ) : 6x 2 - 4 (6x) +1 ( 6* ) ) = 6x2 - 24 x + 6x - 6 x - 30X b . ) Find: (g of ) (x) ( gof ) ( ) = 6 ( x - + 4x+1) 6x + 24 x +6 ( 3 ) ( 2 )9) If m(x) = x3 and n(x) = 16 + x find the function value, if possible. (m - n) (-5) (2-53+6-5 = -5+1 2 10) If m(x) = x - 6 and n(x) = - x - 8 - find the function value, if possible. (nom) (8) 7 - 8 20 ( nom ) = 2 - 6 6 +8 +8 128 - 6 - 2 11) Approximate the function value from the graph. (f + 8) (- 3) 5 f ( * ) = (- 4 ,0 ] y f g(x) 9 ( x ) = ( 213 ) 5 8 5 X y = f(x ) 512) Approximate the function value from the graph. (f g) (-2) 5 yf g ( x) -5 5 X y = f(x) 5 13) The cost in dollars of producing x toy cars is C(x) - 2.2x + 1. The revenue for selling x toy cars is R(x) = 6.45x. To calculate profit, subtract the cost from the revenue. a. Write and simplify a function P that represents profit in terms of x. P ( x ) = ( ( ) - R ( x ) -- 2.2x+1 - 6-45x = ( 4. 2 5X A) 1 b. Find the profit of producing 40 toy cars. P ( 40) 7 -4. 25 ( 40) 7 1 =- 170 + 114) L varies jointly as a and the square root of b. If L = 80 when a = 4 and b = 16, find L when a = = and b = 64. L = 1/2 ( 64 ) 5 L 232 15) The stopping distance of a car varies directly as the square of the speed of the car. If a car traveling 40 mph has a stopping distance of 109 ft, find the stopping distance of a car that travels 25 mph. (Round the answer to one decimal place.) Optional Extra Credit (10 points possible) 16) The volume of a can that is 10 centimeters (cm) tall is approximated by the functionv(r) = 31.472, where r is the radius of the can in cm. Chicken soup costs $0.02 per milliliter (mL) and since 1 mL = 1 cm', we can say that chicken soup costs $0.02 per cm'. The cost to fill a 10 cm tall can with chicken soup is given by C(v) = 0.02v, where v is the volume of the can in cm' a. Find (C ov)(r) and interpret its meaning in the context of this problem. b. Approximate to the nearest cent the cost to fill a 10 cm can with chicken soup if the can's radius is 5 cm. ath 95 Exam 4a/Fall 2023/V.Pace 6