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Learning Target

Learning Target. Students will be able to: Identify independent and dependent variables and write an equation in function notation and evaluate a function for given input values. Determine a relationship between the x - and y- values. Write an equation. 5. 10. 15. 20. 1. 3. 2. 4.

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Learning Target

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  1. Learning Target Students will be able to: Identify independent and dependent variables and write an equation in function notation and evaluate a function for given input values.

  2. Determine a relationship between the x- and y-values. Write an equation. 5 10 15 20 1 3 2 4

  3. Determine a relationship between the x- and y-values. Write an equation. {(1, 3), (2, 6), (3, 9), (4, 12)} x y

  4. The inputof a function is the independent variable. The output of a function is the dependent variable. The value of the dependent variable depends on, or is a function of, the value of the independent variable.

  5. Identify the independent and dependent variables in the situation. A painter must measure a room before deciding how much paint to buy. The amount of paintdependson the measurement of a room. Dependent: amount of paint Independent: measurement of the room

  6. Identify the independent and dependent variables in the situation. The height of a candle decrease d centimeters for every hour it burns. The height of a candledepends on the number of hours it burns. Dependent: height of candle Independent: time

  7. Identify the independent and dependent variables in the situation. A veterinarian must weigh an animal before determining the amount of medication. The amount of medicationdepends on the weight of an animal. Dependent: amount of medication Independent: weight of animal

  8. Helpful Hint There are several different ways to describe the variables of a function. Independent Variable Dependent Variable y-values x-values Domain Range Input Output x f(x)

  9. Identify the independent and dependent variable in the situation. A company charges $10 per hour to rent a jackhammer. The cost to rent a jackhammerdependson the length of time it is rented. Dependent variable: cost Independent variable: time

  10. Identify the independent and dependent variable in the situation. Camryn buys p pounds of apples at $0.99 per pound. The cost of applesdepends on the number of pounds bought. Dependent variable: cost Independent variable: pounds

  11. An algebraic expression that defines a function is a function rule. If x is the independent variable and y is the dependent variable, then function notation for y is f(x), read “f of x,” where f names the function. When an equation in two variables describes a function, you can use function notation to write it.

  12. The dependent variableisa function ofthe independent variable. yisa function ofx. y=f(x) y = f(x)

  13. Identify the independent and dependent variables. Write a rule in function notation for the situation. A math tutor charges $35 per hour. The amount a math tutor charges depends on number of hours. Dependent: charges Independent: hours Let h represent the number of hours of tutoring. The function for the amount a math tutor charges isf(h) = 35h.

  14. Identify the independent and dependent variables. Write a rule in function notation for the situation. A fitness center charges a $100 initiation fee plus $40 per month. The total cost depends on the number of months, plus $100. Dependent: total cost Independent: number of months Let mrepresent the number of months The function for the amount the fitness center charges is f(m) = 40m + 100.

  15. Identify the independent and dependent variables. Write a rule in function notation for the situation. Steven buys lettuce that costs $1.69/lb. The total cost depends on how many pounds of lettuce that Steven buys. Dependent: total cost Independent: pounds Let x represent the number of pounds Steven bought. The function for cost of the lettuce is f(x) = 1.69x.

  16. Identify the independent and dependent variables. Write a rule in function notation for the situation. An amusement park charges a $6.00 parking fee plus $29.99 per person. The total cost depends on the number of persons in the car, plus $6. Dependent: total cost Independent: number of persons in the car Let xrepresent the number of persons in the car. The function for the total park cost is f(x) = 29.99x+ 6.

  17. input x 2 You can think of a function as an input-output machine. 6 function f(x)=5x 5x 10 30 output

  18. Evaluate the function for the given input values. For f(x) = 3x + 2, find f(x) when x = 7 and when x = –4. Evaluate the function for the given input values. For g(t) = 1.5t – 5, find g(t) when t = 6 and when t = –2.

  19. When a function describes a real-world situation, every real number is not always reasonable for the domain and range. For example, a number representing the length of an object cannot be negative, and only whole numbers can represent a number of people.

  20. Joe has enough money to buy 1, 2, or 3 DVDs at $15.00 each. Write a function to describe the situation. Find a reasonable domain and range of the function. y x

  21. Number of watts used is 500timesthe setting #. watts The settings on a space heater are the whole numbers from 0 to 3. The total of watts used for each setting is 500 times the setting number. Write a function rule to describe the number of watts used for each setting. Find a reasonable domain and range for the function. f(x) = 500 •x For each setting, the number of watts is f(x) = 500x watts. HW pp. 249-251/13-23,25-31,36

  22. 1 2 c + b Warm Up Evaluate each expression for a = 2, b = –3, and c = 8. 1. a + 3c 2.ab – c 3. 26 –14 1 4. 4c – b 35 5. ba + c 17

  23. Solve the inequality and graph the solutions.

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