Question

Match each graph with the correct description

Answer 1

For this question you need to be familiar with the basic shapes of odd and even functions; looking at the graphs, we can see that the first two are clearly odd functions and the second two are even functions.

For odd functions, an easy way to tell if it's negative or positive is to see which direction the end of the function on the right side heads in; for the first graph we can see that at x > 1 the gradient is negative, and so the leading coefficient is negative, whilst for the second graph at x > 1 the gradient is positive and so the leading coefficient is positive.

For even functions it would be the same, so for the third graph we can see that the graph has a positive gradient to the right and so the leading coefficient is positive and then for the fourth graph we can see that the graph heads downwards to the right and so the leading coefficient is negative.

So the answers would be:
First graph: The degree of function is odd and the leading coefficient is negative

Second graph: The degree of the function is odd and the leading coefficient is positive

Third graph: The degree of the function is even and the leading coefficient is positive

Fourth graph: The degree of the function is even and the leading coefficient is negative

It is however worth remembering the basic graph of each function that you learn so that these things will become easily identifiable ;)