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Understanding Function Notation in Linear Equations

Learn how to interpret and solve linear functions using function notation, with examples and graphs included. Discover the meaning of f(x) and how to find values for different inputs. Compare flight durations using function formulas.

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Understanding Function Notation in Linear Equations

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  1. Sec 3.3Function Notation

  2. Function Notation - Any linear function can be written in the form f(x) = mx + b f(x) does NOT mean “f times x” f(x) is read as “f of x” f(x) means the same as y Ex #1: Find f(–4), f(0), and f(3) for the function: f(x) = 2x + 7 f(–4 ) means to input –4 for x in the function f(x) = 2x + 7 f(x) = 2x + 7 f(–4) = 2(–4) + 7 = –8 + 7 = –1 f(–4) = –1 f(x) = 2x + 7 f(0) = 2(0) + 7 = 0 + 7 = 7 f(0) = 7 f(x) = 2x + 7 f(3) = 2(3) + 7 = 6 + 7 = 13 f(3) = 13

  3. Interpreting Function Notation Ex #2 Let f(x) be the outside temperature (oF) xhours after 6:00 am. Explain the meaning of each statement. a) f(0) The temperature at 6:00 am b) f(6) = n The temperature at noon is noF c) f(3) <f(6) The temperature at 9:00 am is colder than the temperature at noon.

  4. Using Function Notation to Solve and Graph Ex #3 Using the function , find the value of x when h(x) = –7. Ex #4 Graph f(x) = 2x +5

  5. Ex #5 The graph below shows the number of miles a helicopter is from its destination after x hours on its first flight. On its second flight the helicopter travels 50 miles further and increases its speed by 25 mph. The function f(x) = 350 – 125x represents the second flight, where f(x) is the number of miles the helicopter is from its destination after x hours. Which flight takes less time? Find out how long it takes the second flight to get to its destination by using f(x) = First Flight 0 Distance (miles) The second flight takes less time (2.8 hours compared to 3 hours) Hours

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