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In this last section we have to discuss graphing rational functions. It's is possibly best to begin along a rather simple one that we can do with no all that much knowledge on how these work.
Let's sketch the graph of f ( x ) = 1/x . Firstly, as this is a rational function we will have to be careful with division by zero issues. Thus, we can see from this equation which we'll ought to avoid x = 0 as that will give division by zero.
Now, let's just plug in some of values of x and see what we obtain.
x
f(x)
-4
-0.25
-2
-0.5
-1
-0.1
-10
-0.01
-100
0.01
100
0.1
10
1
2
0.5
4
0.25
Thus, as x get large (positively and negatively) the function keeps the sign of x & gets smaller & smaller. Similarly as we approach x = 0 the function again keeps the similar sign as x however start getting quite large. Following is a sketch of this graph.
Firstly, notice that the graph is into two pieces. Almost all of the rational functions will have graphs in multiple pieces like this.
Next, notice that this graph does not contain any intercepts of any kind. That's simple sufficient to check for ourselves.
if A is an ideal and phi is onto S,then phi(A)is an ideal.
Two sides of an isosceles triangle are 7and 3. The perimeter of the triangle is?
Working together Jack and Bob can clean a place in 30 minutes. On his own, Jack can clean this place in 50 minutes. How long does it take Bob to clean the same place on his own?
x+y=5 Y+-2x+5
We should graph a couple of these to make sure that we can graph them as well. Example : Sketch the graph of the following piecewise function. Solution Now while w
y2/3(y4/3\y1/3
-56
Now we need to discuss the new method of combining functions. The new way of combining functions is called function composition. Following is the definition. Given two functions
x=y=3 , 2x-y=5
How do I solve this factoring X4-x³
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