Question

How does the graph f(x) - g(x) look like? Full question in the description box below.

Answer 1

See the explanation

Explanation:

Firstly the question uses the word 'sketch'. So what you draw does not have to be precise.

Let a sketched point be `P_a`

Suppose we have: `y_1=f(x_1) and y_2=g(x_1)`

So `P_1->f(x_1)-g(x_1)color(white)("ddd")->color(white)("ddd") (x_1,color(white)("d")y_1-y_2)`

Draw (lightly) a series of lines parallel to the y-axis. Where each line crosses the plots project a line parallel to the x-axis such that it meets the y-axis and approximate the value of the relevant `y's->y_1 and y_2`

Then we have `y_("sketch")=[y_1=f(x)]-[y_2=g(x)]` Mark that point. When you have a number of these points sketch a plot through them. I would suggest a coloured pencil.

Looking at your diagram I notice that we have two labelled points that have the same x-value.

`g(x)->(-1,0) and f(x)->(-1,2)`

So for this vertical line we have `f(x)-g(x)-> (x,y)=(-1, color(white)("d")2-0)=(-1,2)`

I also notice that both plots have a shared point (both pass through it) at `P_2->(x,y)=(0,1)` They also have another shared point (`P_3`)that is not labelled. You must make sure your plot passes through each of `P_1,P_2 and P_3`