7.2 Operations with Linear Functions Page 219

Adding Linear Functions You can add and subtract linear functions just as you would add and subtract any two numbers. When adding and subtracting functions, be sure to use a different letter to name each function, like h(x) = f(x) + g(x).

Adding Linear Functions Given f(x) = 5x + 6 and g(x) = 4x -1, find h(x) = f(x) + g(x). Horizontal Method h(x) = f(x) + g(x) h(x) = (5x + 6) + (4x -1)  Substitute for f(x) and g(x) h(x) = 5x + 4x + 6 -1  Combine like terms h(x) = 9x + 5  Simplify.

Adding Linear Functions Given f(x) = 5x + 6 and g(x) = 4x -1, find h(x) = f(x) + g(x). Vertical Method h(x) = f(x) + g(x) 5x + 6 + 4x - 1 9x + 5 Therefore, h(x) = 9x + 5. Line them up by like terms.

Subtracting Linear Functions When subtracting linear functions, reverse the sign of each term of the second function. Then add the functions. Given f(x) = 12x + 3 and g(x) = 16x - 4, find h(x) = f(x) – g(x). Horizontal Method h(x) = f(x) – g(x) h(x) = (12x + 3) – (16x - 4) Substitute for f(x) and g(x) h(x) = 12x + 3 + (-16x + 4)  Reverse the signs on the 2nd function h(x) = 12x + (-16x) + 3 + 4  Combine like terms h(x) = -4x + 7  Simplify

Subtracting Linear Functions Given f(x) = 12x + 3 and g(x) = 16x - 4, find h(x) = f(x) – g(x). Vertical Method 12x + 3 12x + 3 - (16x - 4) +-16x + 4 -4x + 7 h(x) = -4x + 7 Reverse the signs of the second term. 

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Multiplying Linear Functions Multiplying a linear function by a constant function is just like multiplying two expressions together. When you multiply a linear function by a constant, the result is also a linear function.

Multiplying Linear Functions Given f(x) = 6 and g(x) = 4x – 3, find h(x) = f(x) × g(x). h(x) = f(x) × g(x) h(x) = 6 × (4x – 3)  Substitute for f(x) and g(x) h(x) = (6)4x – (6)3  Use the Distributive Property h(x) = 24x – 18  Simplify.

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Real-World Problem (Word Problem – Your Favorite ) A company that makes jerseys for sports teams charges a set up fee of $35 per order plus $10 for each shirt. If the shirts have to be shipped to the customer, the shipping charge is $8 plus $0.50 per shirt. Find the total amount that a team would pay as a function of x, the number of shirts ordered.

Step1: Write f(x), the cost of the team jerseys. $35 per order plus $10 for each shirt f(x) = 35 + 10x Step 2: Write g(x), the cost of shipping the jerseys. $8 plus $0.50 per shirt g(x) = 8 + 0.50x Step 3: Write t(x), the total cost of the shirts and shipping, as a function of x. t(x) = f(x) + g(x) t(x) = 35 + 10x + 8 + 0.50x  Substitute for f(x) and g(x) t(x) = 35 + 8 + 10x + 0.50x  Combine like terms t(x) = 43 + 10.5x  Simplify The total cost is 43 + 10.5x.

Real-World Problem (Another Word Problem – Your Favorite ) Miguel sells sandwiches in the park. Each sandwich costs $3.75. He has 4 customers who get a sandwich every day. If he sells sandwiches to x additional customers, find the total amount that Miguel will make in a day. Step1: Write f(x), the cost of each sandwich. f(x) = $3.75

Step 2: Write g(x), the amount of customer he serves daily. 4 plus x additional customers g(x) = 4 + x Step 3: Write t(x), the total cost of the shirts and shipping, as a function of x. t(x) = f(x) × g(x) t(x) = 3.75(4 + x)  Substitute for f(x) and g(x) Miguel will make 3.75(4 + x) in a day.

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