Step 1: Graph the Area (using Desmos): This confirms that we are dealing with a negative area under the x-axis. In other to get a positive value we have to put a negative sign in front of the integral: In other words, you’re taking the negative of the integral solution (a negativ...
The following examples are based on this graph of a piecewise function which has a jump at x = 1: Example question 1: What is the limit of f(x) as x approaches 2? Solution:“f(x)” is the function value at 2 (a.k.a. the y-value). We want to know what’s happening to the...
But the College Board still has to make the test difficult to differentiate student skill levels, sothe SAT needs to test these concepts in strange ways. This trips up students who don't prepare, but it rewards students who understand the test well. Here's an example: Find the area of t...
shaded area is z > -0.8 Step 2: Visit the normal probability area index and find a picture that looks like your graph. Follow the instructions on that page to find the z-value for the graph. The z-value is the probability. Tip: Step 1 is technically optional, but it’s always a...
Using transformations to graph functionsSometimes we can use the concept of transformations to graph complicated functions when we know how to graph the simpler ones.For example, if you know the graph of f(x), the graph of f(x) + c will be the same function, just shifted up by c ...
Anabsolute value functionhas a unique “V” shape when plotted on a graph. This is due to the fact that the absolute value of a negative number makes that number positive. The absolute value parent function. The absolute value parent function is written as: f(x) = │x│ where: ...
Note: If the bounds of integration aren’t integers (the second integral here has e, Euler’s number), you may want to use a graphing calculator (I used the one at Desmos.com to draw this graph) so you can more easily sketch the shape. Step 3: Find the shaded area that meets the...
The lowest point on a graph is called theminima; the highest point on a graph is called themaxima. “Global means “the entire graph of the function” while “local” refers to “a small part of the graph”. Image Source: https://en.wikipedia.org/wiki/Maxima_and_minima ...
Step 1:Create a graph to help you visualize the problem.I usedDesmos.com: By looking at the intersections of the two functions, I can see that the two graphs form a leaf-like shape between x = 0 and x = 1. This is the shape we’re going to rotate. The interval from 0 to 1 ...