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Understanding Functions and Variables in Algebra

Learn to identify independent and dependent variables, write equations in function notation, and evaluate functions with given input values in algebra. Gain mastery over key vocabulary and essential concepts.

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Understanding Functions and Variables in Algebra

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  1. 3-3 Writing Functions Holt Algebra 1 Warm Up Lesson Presentation Lesson Quiz Holt McDougal Algebra 1

  2. Objectives Identify independent and dependent variables. Write an equation in function notation Evaluate a function for given input values.

  3. Vocabulary independent variable dependent variable function rule function notation

  4. Input /Independent Domain x function f(x) y Range Output /Dependent

  5. Identify the independent and dependent variables. • A painter must measure a room before deciding how much paint to buy. The amount of paintdepends on the size of a room. Dependent: amount of paint Independent: measurement of the room 2) The height of a candle decreases d centimeters for every hour it burns. The height of a candledependson the # of hours it burns. Dependent: height of candle Independent: # of hours

  6. 3) 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 4) Apples cost $0.99 per pound. The cost of applesdepends on the number of pounds bought. Dependent variable: cost Independent variable: pounds

  7. 10 – 4 2 5 – 4 = 1 or Determine a relationship between the x- and y-values. 5 10 15 20 1 3 2 4 Step 1 List possible relationships between the first x and y Step 2 Write an equation. or f(x) = (1/5)x function notation Read as: f of x / function of x

  8. {(1, 3), (2, 6), (3, 9), (4, 12)} x 4 1 2 3 y 3 6 9 12 Step 1 List possible relationships between the first x and y 1  3 = 3 or 1 + 2 = 3 2 • 3 = 6 2 + 2 6 Step 2 Write an equation. y = 3x or f(x) = 3x function notation Read as: f of x / function of x

  9. Identify the independent and dependent variables. Write an equation in function notation for the situation. A math tutor charges $35 per hour. Dependent: fee Independent: hours Let h represent the number of hours of tutoring. The function isf(h) = 35h A fitness center charges a $100 initiation fee plus $40 per month. Dependent: total cost Independent: number of months Let mrepresent the number of months The function is f(m) = 40m + 100.

  10. You can think of a function as an input-output machine. For Tasha’s earnings, f(x) = 5x. If you input a value x, the output is 5x. input x 2 6 function f(x)=5x 5x 10 30 output

  11. WARM UP Look at the pattern 1) Draw the 5th and the 6th figures. 2) Use the table to fill in the information • 3) Write an equation to show the relationship between x and y • 4) How many squares will be used in the 20th figure?

  12. Identify the independent and dependent variables. Write an equation in function notation for the situation. 1) A math tutor charges $35 per hour. y Dependent: fee Independent: hours x The function isy = 35x ORf(x) = 35x 2) A fitness center charges a $100 initiation fee plus $40 per month. y Dependent: total cost Independent: number of months x The function is y = 40x + 100 OR f(x) = 40x + 100

  13. Adnoc needed National day presents for their office staff. The cost was 150 DHS per staff member present. They also had to pay 750 DHSto have it all shipped from abroad. • a) Identify the dependent and Independent Variables. • b) Write an equation in function for this situation • c) If they bought 250 presents, how much did it cost? • d) If they had 3250 DHS to spend, how may presents could they buy?

  14. Evaluating Functions You can think of a function as an input-output machine. For Tasha’s earnings, f(x) = 5x. If you input a value x, the output is 5x. input x 2 6 function f(x)=5x 5x 10 30 output

  15. Evaluate the function for the given input values. f(7) f(-4) f(x) = 3x + 2, find f(x) when x = 7 and when x = –4 f(x) = 3(x) + 2 f(x) = 3(x) + 2 = 3(–4) + 2 = 3(7) + 2 = –12 + 2 = 21 + 2 = 23 = –10

  16. Evaluate the following expressions given the functions below: g(x) = -3x + 1 f(x) = x2 + 7 h(x) = 12/x j(x) = 2x + 9 • a) g(10) • b) f(3) • c) h(-2) • d) j(7) • e) h(-4)

  17. The flu has spread throughout a town. The function below determines how many people have the flue, where t=time in days and f(t)=the number of people in thousands. f(t) = 3t – 5 • a) find f(6) • b) what does f(2) mean? c) Find t when f(t) = 16

  18. Lesson Quiz: Part I Identify the independent and dependent variables. Write an equation in function notation for each situation. 1. A buffet charges $8.95 per person. independent: number of people dependent: cost f(p) = 8.95p 2. A moving company charges $130 for weekly truck rental plus $1.50 per mile. independent: miles dependent: cost f(m) = 130 + 1.50m

  19. Lesson Quiz: Part II Evaluate each function for the given input values. 3. For g(t) = , find g(t) when t = 20 and when t = –12. g(20) = 2 g(–12) = –6 4. For f(x) = 6x – 1, find f(x) when x = 3.5 and when x = –5. f(3.5) = 20 f(–5) = –31

  20. Lesson Quiz: Part III Write a function to describe the situation. Find the reasonable domain and range for the function. 5. A theater can be rented for exactly 2, 3, or 4 hours. The cost is a $100 deposit plus $200 per hour. f(h) = 200h + 100 Domain: {2, 3, 4} Range: {$500, $700, $900}

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