output f

Name: ____________________________
Period: __________
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.
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?