Find the value of the function 𝑓 of 𝑥 for the input given using the function machine.
So in this question, we have a function machine. And a function machine is simply a diagram representing a machine which takes an input, applies a function or a rule, and produces an answer or an output. In this slightly more complex example of a function machine, the input can be represented by 𝑥, the function is our value 𝑓, and the output would be 𝑓 of 𝑥. The notation 𝑓 of 𝑥 refers to the fact that our function 𝑓 is related to the input 𝑥.
So, let’s take an example of a simpler function, and let’s say that we have 𝑓 of 𝑥 equals two plus 𝑥. Then, if we took an input of 𝑥 equals three, and we would therefore be working out 𝑓 of three. And to do this, we simply replace or substitute all the values of 𝑥 with the value of three, which would give us two plus three. And therefore, 𝑓 of three would be equal to five. So, let’s now return to the question and have a look at the function of 𝑥 in this case.
Here we have the 𝑓 of 𝑥 equals 𝑥 squared plus 𝑥. And the input we’re asked to compute it for is 𝑥 equals negative three. This means that we’re calculating 𝑓 of negative three. So, substituting our value 𝑥 equals negative three, we would have negative three all squared plus negative three. This would simplify to nine, since negative three times negative three gives us nine, subtract three, since our positive and negative signs here are equivalent to a negative or a subtraction. And we can evaluate this as six. So, the value of our function 𝑓 of 𝑥 for the input of negative three is six.