Question

What does a function’s end behaviour mean?

Answer 1

From the given question we have been asked to explain the end behaviour of a function. We will explain the concept of end behaviour of a function. We will take an example and find the end behaviour of that function and thus we solve the given question briefly. So, we proceed with our solution as follows.

Complete step by step solution:
The end behaviour of a function is the behaviour of the graph of the function $f\left( x \right)$ as it approaches positive infinity or negative infinity.
This is determined by the degree and the leading coefficient of a polynomial function.
For example we will assume a function and explain the end behaviour of the function briefly.
$\Rightarrow y=f\left( x \right)=\dfrac{1}{x}$
For this assumed function as $\Rightarrow x\to \infty ,f\left( x \right)\to 0$
The graph of the will be as follows.

Here from this graph we can see that as the value of x approaches infinity the values of y that is the function value is approaching zero.

Note:
Students must be able to understand the given question. Students must have good knowledge in the concept of functions mainly the behaviour of the function at different values of x. in the above example the function have two branches but we have to notice that as we are discussing about the end behaviour, we could be able to say that as x tends to positive infinity and also negative infinity the value of function will tend to zero.