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ACT Test Prep I-2

ACT Test Prep I-2. 3 x ³ ·2 x ² y ·4 x ² y is equivalent to: F. 9 x⁷y² G. 9 x¹²y² H. 24 x⁷y² J. 24 x¹²y K. 24 x¹²y². 1.2 Composition of Functions. Operations with Functions. Sum: Difference: Product: Quotient:. Example 1:.

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ACT Test Prep I-2

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  1. ACT Test Prep I-2 3x³ ·2x²y ·4x²y is equivalent to: F. 9x⁷y² G. 9x¹²y² H. 24x⁷y² J. 24x¹²y K. 24x¹²y²

  2. 1.2Composition of Functions

  3. Operations with Functions • Sum: • Difference: • Product: • Quotient:

  4. Example 1: Given f(x) = 2x – 1 and g(x) = x², find each function. • (f + g) (x) • (f - g) (x) • (f · g) (x) d.

  5. More examples: Given f(x) = 3x² + 4x – 5 and g(x) = 2x + 9, find each function. • (f + g) (x) • (f - g) (x) • (f · g) (x) d.

  6. For the Lotsa Coffee Shop, the revenue r(x) in dollars from selling x cups of coffee is r(x)=1.5 x. The cost c(x) for making and selling the coffee is c(x) = 0.2x + 110. • Write the profit function • Profit function = revenue – cost: p(x) = r(x) – c(x) • Find the profit on 100, 200, and 500 cups of coffee sold.

  7. Composition of Functions The term "composition of functions" (or "composite function") refers to the combining of functions in a manner where the output from one functionbecomes the input for the next function. In math terms, the range (the y-value answers) of one function becomesthe domain (the x-values) of the next function 

  8. The notation used for composition is: (f ◦g) (x) = f (g(x)) and is read "f composed with g of x" or "f of g of x". Notice how the letters stay in the same order in each expression for the composition. f (g(x))clearly tells you to start with function g (innermost parentheses are done first).

  9. Examples Find (f ◦ g)(x) and (g ◦ f)(x) for each f(x) and g(x). • f(x) = 2x + 5 g(x) = 3 + x • f(x) = 2x – 3 g(x)= x² - 2x 3. f(x) = x² - 2x g(x)= 3x

  10. Domains of a Composition The domain of a composed function (f ◦ g)(x) is determined by the domains of f(x) and g(x). For example: State the domain of (f ◦ g)(x) for f(x) = g(x) =

  11. State the domain of (f ◦ g)(x) for: • f(x) = g(x) = x + 3 • f(x) = g(x) = 7 - x

  12. Assignment Pages 17 -18 12 – 24 even 39 Write the functions of each problem and show all work.

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