//Question number 1//
When graphing an inequality there are certain things to keep in mind that make it different from an equation of a line.
Here are some of them:
*You must look out to see whether it will be dashed or solid
*You must know which side of the graph to shade it in
*If they are not in standard form, you have to change them into standard form (THIS ONE MIGHT ACTUALLY APPLY TO A REGULAR EQUATION)
----Basically, the main difference is that in a "normal equation" you have an equal sign while in an inequality you have inequality signs (≤, ≥, <, >)----
//Question Number 2//
------ When using ≤ or ≥ (where they have half the equal sign at the bottom) the line for the inequality would be solid
------ When using < or > (where there is no equal sign- just the inequality sign) the line for the inequality would be dashed
------------------BY THE WAY, I INCLUDED AN ILLUSTRATIO OF AN INEQUALITY GRAPH TO GO ALONG WITH THE 3RD QUESTION----------------
Let that be
Two vertical asymptotes at -1 and 0
If we simply
Find a equation
Find zeros
Horizontal asymptote
So our equation is
Graph attached
a) The first integral corresponds to the area under y = f(x) on the interval [0, 3], which is a right triangle with base 3 and height 5, hence the integral is
b) The integral is zero since the areas under the curve over [3, 4] and [4, 5] are equal but opposite in sign. In other words, on the interval [3, 5], f(x) is symmetric and odd about x = 4, so
c) The integral over [5, 9] is the negative of the area of a rectangle with length 9 - 5 = 4 and height 5, so
Then by linearity, we have