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Understanding Function Operations: Sum, Difference, Product, Quotient

Learn how to perform operations on functions such as sum, difference, product, and quotient. Understand the concept of functions and their domains and ranges. Practice evaluating functions and compositions for various inputs.

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Understanding Function Operations: Sum, Difference, Product, Quotient

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  1. 7.3 Power Functions & Function Operations p. 415

  2. Sum : f(x) + g(x) = (f+g)(x) Difference : f(x) - g(x) = (f-g)(x) Product : f(x) * g(x) = (fg)(x) Quotient :

  3. f(x) = 2x – 3 and g(x) = Sum Difference Product Quotient

  4. Functions In order for a relationship to be a function… EVERY INPUT MUST HAVE AN OUTPUT TWO DIFFERENT INPUTS CAN HAVE THE SAME OUTPUT ONE INPUT CAN HAVE ONLY ONE OUTPUT INPUT (DOMAIN) FUNCTIONMACHINE OUTPUT (RANGE)

  5. Look on page 67 • No two ordered pairs can have the same first coordinate (and different second coordinates).

  6. Time of Day Degrees C 3 15 1 6 2 4 9 1 11 4 12 7 6 13 2 5 10 3 8 5 14 Domain Inputs: 1,2,3,4,5,6 Contains the Range Outputs: 9,10,12,13,15

  7. Ex. Is this a function? {(2,5) , (3,8) , (4,6) , (7, 20)} {(1,4) , (1,5) , (2,3) , (9, 28)} {(1,0) , (4,0) , (9,0) , (21, 0)}

  8. Notation “f of x” Input = x Output = f(x) = y

  9. Ex: Let f(x)=3x1/3 & g(x)=2x1/3. Find (a) the sum, (b) the difference, and (c) the domain for each. • 3x1/3 + 2x1/3 = 5x1/3 • 3x1/3 – 2x1/3 = x1/3 • Domain of (a) all real numbers Domain of (b) all real numbers

  10. Ex: Let f(x)=4x1/3 & g(x)=x1/2. Find (a) the product, (b) the quotient • 4x1/3 * x1/2 = 4x1/3+1/2 = 4x5/6 = 4x1/3-1/2 = 4x-1/6 =

  11. Evaluate (f-g)(x) when x = 2 for the functions (f - g)(x) = (f - g)(2) =

  12. Composition • f(g(x)) means you take the function g and plug it in for the x-values in the function f, then simplify. • g(f(x)) means you take the function f and plug it in for the x-values in the function g, then simplify.

  13. The COMPOSITION of the function f with g is Plug the second function into the first

  14. Evaluate the following when x = 0, 1, 2, 3 given that

  15. Ex: Let f(x)=2x-1 & g(x)=x2-1. Find (a) f(g(x)), (b) g(f(x)), (c) f(f(x)) (a) 2(x2-1)-1 = (c) 2(2x-1)-1 = 2(2-1x) = (b) (2x-1)2-1 = 22x-2-1 =

  16. A clothing store is having a sale in which you can take $50 off the cost of any coat in the store. The store also offers 10% off your entire purchase if you open a charge account. You decide to open a charge account and buy a coat. Use composition of functions to find the sale price of a $175 coat when $50 is subtracted before the 10% discount is applied.

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