Name: ____________________________ Period: __________ 1-34. FUNCTION MACHINES A function works like a machine, as shown in the diagram below. A function is given a name that can be a letter, such as f or g. The notation represents the output when x is processed by the machine. (Note: f(x) is read, “f of x.”) When x is put into the machine, , the value of a function for a specific x-value, comes out. In this notation, f(x) replaces y. For example, y = 3x – 1 andf(x) = 3x – 1 are equivalent ways to write the same function. Numbers are put into the function machine (in this case, f(x) = 3x – 1) one at a time, and then the function performs the operation(s) on each input to determine each output. For example, when x = 3 is put into the function f(x) = 3x – 1, the function triples the input and then subtracts 1 to get the output, which is 8. The notation f(3) = 8 shows that when a 3 is input into the function named f, the output is 8. a. Calculate the output for f(x) = 3x – 1 when the input is x = 14; that is, find f(14). b. Now find the value of f(–10). c. If the output of this function is 24, what was the input? That is, if f(x) = 24, then what was x? Is there more than one possible input? 1-35. Determine the relationship between x and f(x) in the table below and write the equation. 1-36. Determine the corresponding outputs or inputs for the following functions. If there is no possible output for the given input, explain why not. a. b. c. d. e. f. g. h. i. 1-37. Examine the function defined above. Notice that g(2) = 5. That is, when the input x is 2, the output g(2) is 5 a. When the input is 1, what is the output of the function? That is, find the value of g(1). b. Likewise, what are g(–1) and ? g(0) c. What is the input of this function when the output is –2.5? In other words, find the value of x when g(x) = –2.5. Is there more than one possible solution?