# Question Video: Recognizing the Relationship between the Input and Output of a Function Mathematics • 9th Grade

Given the function π, the meaning of π(π β 1) is βthe output when the input is 1 less than πβ. Interpret the following. 1) π(π + 3). 2) π(π ) β 3. 3) π(3 β π₯). 4) π(π) β π(π). 5) π(3π‘). 6) π(π)^π.

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### Video Transcript

Given the function π, the meaning of π of π minus one is the output when the input is one less than π. Interpret the following. π of π plus three, π of π  minus three, π of three minus π₯, π of π minus π of π, π of three π‘, and π of π to the power π.

Before starting this question, it is worth recalling what we mean by a function π. If we have any function π of π₯, then π₯ is the input and π of π₯ is the output. A number inside the bracket affects the input, whereas a number outside of the bracket affects the output. This can be seen from the example, as π minus one means one less than π.

Our first function, π of π plus three, is very similar to the example. Instead of subtracting one from π, weβre adding three to π. This means that π of π plus three calculates the output when the input is three more than π.

Our second function, π of π  minus three, is slightly different. This time, the three that is being subtracted is outside of the bracket. π of π  will be the output when the input is π . Therefore, π of π  minus three is three less than the output when the input is π .

Our third function, π of three minus π₯, is very similar to the first one and also the example. This time, our function gives us the output when the input is π₯ less than three. We are subtracting π₯ from three and then working out the output.

Our fourth function has two variables, π and π. We have π of π minus π of π. This means that we are subtracting the value of π of π from the value of π of π. This is the difference between them. Therefore, the answer corresponds to the change in output when the input changes from π to π.

The penultimate function is π of three π‘. We are multiplying our value of π‘ by three. This is a similar idea once again to our first function, π of π plus three, and also our third function, π of three minus π₯. This time, it corresponds to the output when the input is three times π‘.

Our final function involves exponents or powers. We have π of π to the power of π. As the π is outside of the bracket or parentheses, this is the result of raising the output at input π to the πth power. If the power π was inside the bracket, we would be raising the input to the πth power. Interpreting and often drawing functions of this type is an important part of the topic.