Answer:
1) When we have a function y = f(x), evaluating this function in one given point (x0 for example ) is equivalent to changing the x inside the function by the value x0.
This will give us the point (x, f(x0)).
now, a graph is conformed by the set of all the points (x, f(x)).
2) The x and y-intercepts are the points where the graph intercepts the x-axis or the y-axis.
If you have a table with points (x, y), the y-intercept is the point (0, y') and the x-intercept is the point (x', 0)
Where x' and y' are known values.
If you have an equation:
y = f(x).
The x-intercept is the point (x', 0)
So you need to find the value x' such that f(x') = 0.
The y-intercept is the point (0, y')
So you need to evaluate the function in x = 0, and find the value of y.
y' = f(0).
3) The obvious answer is any science-related career, where graphs are used to transmit a lot of information with almost no words.
Another option can be an economist, where, for example, interpreting and comparing graphs can be useful to determine which option fits better the needs of a given company or what decision is better to be taken.