### 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,
weβre 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 πth
power. If the power π was inside the
bracket, we would be raising the input to the πth power. Interpreting and often drawing
functions of this type is an important part of the topic.