Algebra 1 Module 2 Test Review

Algebra 1 Module 2 Test REVIEW Investigations 1-5 Name: __Answers___ Date: _________ Period: ___ 1. Water is draining from a 780-gallon tank at a rate of 12 gallons per minute. Let y represent the total number of gallons that have drained from the tank and let x represent the number of minutes elapsed since the water started draining. a. Define a function f that has the number of minutes elapsed since the water started draining from the tank as its input and the total number of gallons of water that have drained from the tank as its output. f(x) = 12x b. What is the domain of f? (What values can the number of minutes the water has been draining take on in this situation?) 0 ≤ x ≤ 65 c. What is the range of the function f? (What values can the total number of gallons drained from the tank take on in this situation?) 0 ≤ f(x) ≤ 780 d. Express the number of gallons drained from the tank 31.5 minutes after the water started draining using function notation. f(31.5) e. Explain what f (32) represents in the context of this problem. f(32) gallons have drained after 32 minutes f. What does the value of x in the equation f(x) = 468 represent? 468 gallons drained after 39 minutes 2. Let f(x) = 4(2 - x) + 7 a. Determine the given values: f(-3) = 4(2-(-3)) + 7 4(5) + 7 20 + 7 f(-3) = 27 f(5) = 4(2-(5)) + 7 4(-3) + 7 -12 + 7 f(-3) = -5 f(2) = 4(2-(2)) + 7 4(0) + 7 0+7 f(-3) = 7 3. Given that the following graphs represent how two quantities change together, determine whether or not each graph represents a function. If the graph represents a function, determine the domain of the function and the range of the function. If the graph does not represent a function, explain why. i. Function: Yes/No Explain. For every input there is exactly one output i. Function: Yes/No Explain For every input there is exactly one output Domain: ___-3 ≤ x ≤ 3 Domain: __-12 ≤ x ≤ 8 Range: _____-2 ≤ y ≤ 2 Range: _____4 ≤ y ≤ 8_ 4. Determine if the following are functions or not. If they are determine the domain and range. a. x y -2 2 -1 0 0 -2 -1 2 Not a function, -1 has output of 0 & -2 Yes a function Domain: -∞ ≤ x ≤ ∞ Rnage: 0≤ x ≤ ∞ b. x y -4 2 -2 8 -1 12 -2 20 Not a function, -1 has output of 0 & -2 Yes a function Domain: -∞ ≤ x ≤ ∞ Rnage: -∞ ≤ x ≤ ∞ No not a function 5. For each of the given functions, determine the horizontal intercepts and vertical intercepts. Graph each function. State if the given function is increasing or decreasing. a. g(x) = 2x + 3 0 = 2x + 3 -3 = 2x x = -1.5 Horizontal: (-1.5,0) b. h(x) = f(x) = 2(0)+ 3 f(x) = 0 + 3 f(x) = 0 Vertical Int (0,3) 3 x−4 4 0 = 3/4x - 4 4 = 3/4x 16 = 3x x = 5.3 Horz (5.3, 0) f(x) = ¾(0)- 4 f(x) = 0 - 4 f(x) = -4 Vert (-4,0) b. a. Increasing or Decreasing Increasing or Decreasing 6. John is going to run a half marathon (13.1 miles). Based on his weight and speed, he will burn 105 calories per mile. a. Define a function f that determines the total number of calories John has burned in terms of the number of miles x he has run. Define your variables f(x) = the total number of calories John has burned x = the number of miles x he has run f(x) = 105x b. Evaluate f(2) and explain what the value represents. John burned f(2) calories after 2 miles f(2) = 210 c. What is the maximum value of the function f? What does the maximum value represent? 1375.5 calories because a marathon is 13.1 miles. d. Is f(15) a possible value? Why or why not? No most miles is 13.1 7. Describe the change in distance with regards to the calories burned from the above example? As the number of miles increase the number of calories burned increases.