# MATH 107 Quiz 5

MATH 107 Quiz 5 MATH 107_SU21 QUIZ 5 Name:______________________ Date:_____________ Please show your work for all problems, and express your answers using exact values. Express fractions in simplest form, including rationalizing all denominators. Problem/Solution 1 score Given the functions π(π₯) = β 3 βπ₯ and π(π₯) = 3π₯ 2 β 1, find the following values if they exist. a) (π β π)(3) b) (π β π)(β1) 4 c) (π β π) (9) β2 d) (π β π) ( 3 ) 2 2π₯ π₯ Given the functions π(π₯) = and π(π₯) = , find and simplify the following π₯+2 2π₯β1 functions, then state the domain of each in interval notation. a) (π β π)(π₯) b) (π β π)(π₯) 3 Determine whether the function β(π₯) = 2π₯+9 is π₯β3 one-to-one a) analytically, by testing β(π) = β(π) b) graphically, by using the horizontal line test Page 1 of 3 MATH 107 Quiz 5 4 3βπ₯ Given the one-to-one function π(π₯) = π₯+3 a) State the domain and range of the function in interval notation. b) Find the inverse, π β1 (π₯). c) Check your answer using function composition. 5 Continuation of question 4 d) Find the vertical and horizontal asymptotes for π(π₯) and π β1 (π₯). e) Graph π(π₯) and π β1 (π₯) on two separate graphs. Include the asymptotes as dashed lines. f) 6 Identify and label the coordinates of 3 points on the graph of π(π₯). Reverse the x and y coordinates, then plot these points on the graph of π β1 (π₯) to confirm this is the inverse function. The wind chill can be calculated as π = 35.74 + 0.6215ππ β 35.75π 0.16 + 0.4275ππ π 0.16 where W is the wind chill temperature in degrees Fahrenheit, Ta is the air temperature in degrees Fahrenheit, and V is the wind speed in miles per hour. The formula is valid when ππ β€ 50β and π > 3 mph. a) If the air temperature is 36β and the wind speed is 14 mph, what is the wind chill temperature? Express your answer as a complete sentence and round to two decimal places. b) If the air temperature is 40β and the meteorologist says it will feel like 32β, what is the wind speed? Express your answer as a complete sentence and round to two decimal places. 7 Continuation of question 6 Page 2 of 3 MATH 107 Quiz 5 c) Write and simplify the formula for W as a function of wind speed, π(π), when the air temperature is ππ = 20β. Show your work! d) Find the value of V when π(π) = 0. Then write a sentence interpreting what this means. 8 Find all real solutions. Check your solutions in the original equation to see which are true and which are extraneous. 3π₯ β 2 β β2 β π₯ = π₯ β 1 9 A $1400 check is deposited in an account earning 1.4% interest compounded monthly. a) Write the equation for the amount A in the account as a function of investment time in years, t. b) Determine how much is in the account after 5 years, 10 years, and 20 years. Round your answers to the nearest cent. c) Using your equation from part a), determine how long it will take for the investment to reach $2100. Round your answer to the nearest hundredth of a year. 10 Simplify the following expressions. 1 ) 625 a) log 5 ( b) log 3 (β27) c) log 1 (32) 2 Page 3 of 3

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