We have a polynomial m(x). We do not know by now its equation, but we can look for that information asked in the graph.
a) End behaviour:
This is referring to the values of the function when x tends to minus infinity and also infinity.
When x becomes really small, the graph indicates that m(x) increases infinitely.
The same happens when x becomes really big.
Both conditions are indicated with arrows at the end of the line.
So the end behaviour is:
- m(x) increases when x tends to minus infinity.
- m(x) increases when x tends to infinity.
b) y-intercept:
Is the value of the function where the function intersects the y-axis. It can also be expressed as m(0), as this is the value of x where the y-axis is located.
This happens at (0,0), so the the y-intercept is y=m(0)=0.
c) x-intercepts:
When m(x) intersects the x-axis, we have the zeros or roots, also called x-intercepts.
In this function we have 4 x-intercepts at points (-4,0), (-3,0), (0,0) and (2,0).
The x-intercepts then are located at x=-4, x=-3, x=0 and x=2.
d) Domain:
This is the set of values of x for which the function m(x) is defined.
There is no discontinuity present in the graph, so we can assume that the domain of m(x) is all the real numbers.
Domain = (-∞, ∞).
e) Range:
This is the set of values that m(x) can take for the values of x for which it is defined. In this case, we are sure we have a minimum value of m(x) at x=1, where m(1) = -21.
There is no defined maximum and the arrows indicate that the function continously increases for both ends, so the maximum limit for the range is written as infinity.
Then, we can define the range as [-21,∞).