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Understanding Functions: Examples and Applications

Learn about finding function values, creating function tables, identifying independent and dependent variables, analyzing domains and ranges, and writing and evaluating functions through real-world examples.

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Understanding Functions: Examples and Applications

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  1. Lesson Menu Main Idea and New Vocabulary Example 1: Find a Function Value Example 2: Make a Function Table Example 3: Real-World Example: Independent and Dependent Variables Example 4: Real-World Example: Analyze Domain and Range Example 5: Real-World Example: Write and Evaluate a Function

  2. Complete function tables. • function • function table • independent variable • dependent variable Main Idea/Vocabulary

  3. Find a Function Value Find f(–6) if f(x) = 3x + 4. f(x) = 3x + 4 Write the function. f(–6) = 3(–6) + 4 Substitute –6 for x into the function rule. f(–6) = –18 + 4 or –14 Simplify. Answer:So, f(–6) = –14. Example 1

  4. Find f(–2) if f(x) = 4x + 5. A.–13 B. –3 C. 3 D. 13 Example 1 CYP

  5. Make a Function Table Choose four values for x to make a function table for f(x) = 4x – 1. Then state the domain and range of the function. Substitute each domain value x into the function rule. Then simplify to find the range value. Answer:The domain is {–2, –1, 0, 1}. The range is {–9, –5, –1, 3}. Example 2

  6. Use the values –2, –1, 0, 1 for x to make a function table for f(x) = 2x + 3. State the domain and range of the function. A. domain: {−2, −1, 1}range: {0, 1, 3, 5} B.domain: {–2, –1, 0, 1}range: {–1, 1, 3, 5} • domain: {–2, –1, 0, 1}range: {1, 3, 5} D.domain: {–1, 1, 3, 5}range: {–2, –1, 0, 1} Example 2 CYP

  7. Independent and Dependent Variables FOODLinda buys a can of tuna fish that weighs 4.2 ounces. The total weight w of any number of cans c of tuna fish can be represented by the function w(c) = 4.2c. Identify the independent and dependent variables. Answer:Since the total weight of the cans depends on the number of cans, the total weight w is the dependent variable and the number of cans c is the independent variable. Example 3

  8. FOODThere are approximately 275 miniature marshmallows in a 10.5-ounce bag of marshmallows. The total number of marshmallows m in any number of bags b can be represented by the function m(b) = 275b. Identify the independent and dependent variables. A.The number of marshmallows m is the dependent variable. The number of bags b is the independent variable. B.The number of bags b is the dependent variable. The number of marshmallows m is the independent variable. Example 3 CYP

  9. Analyze Domain and Range FOODLinda buys a can of tuna fish that weighs 4.2 ounces. The total weight w of any number of cans c of tuna fish can be represented by the function w(c) = 4.2c.What values of the domain and range make sense for this situation? Explain. Answer:Only whole numbers make sense for the domain because you cannot buy a fraction of a can of tuna fish. The range values depend on the domain values, so the range will be rational number multiples of 4.2. Example 4

  10. FOODThere are approximately 275 miniature marshmallows in a 10.5-ounce bag of marshmallows. The total number of marshmallows m in any number of bags b can be represented by the function m(b) = 275b. What values of the domain and range make sense for this situation? Explain. • Only positive rational numbers make sense for the domain. The range will be multiples of 275. B.Only whole numbers make sense for the domain. The range will be multiples of 10.5. C.Only whole numbers make sense for the domain. The range will be multiples of 275. D.The domain will be multiples of 275. The range will be whole numbers. Example 4 CYP

  11. Write and Evaluate a Function DANCEA dance studio charges an initial fee of $75 plus $8 per lesson. Write a function to represent the cost c(ℓ) for ℓlessons. Then determine the cost for 13 lessons. The function c(ℓ) = 8ℓ + 75 represents the situation. Example 5

  12. Write and Evaluate a Function To find the cost for 13 lessons, substitute 13 for ℓ. c(ℓ) = 8ℓ + 75 Write the function. c(ℓ) = 8(13) + 75 or 179 Substitute 13 for ℓ. Answer:It will cost $179 for 13 lessons. Example 5

  13. PHOTOGRAPHY A photographer charges a $55 sitting fee plus $15 for each pose. Write a function to represent the cost c(p) for p poses. Then determine the cost for 8 poses. A.c(p) = 55c + 15; $455 B.c(p) = 15c + 55; $175 C.c(p) = 55p + 15; $455 D.c(p) = 15p + 55; $175 Example 5 CYP

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