What is the graph of the function f(x) = the quantity of x plus 4, all over x plus 6?
1 answer:
I've downloaded a graph for you. It is one of the first things you should always think about with a question like this one. You should notice the following about it:
1. The denominator gives a discontinuity point at (x = - 6). You can tell that is happening just by looking at the graph at x = - 6. The range at that point is - infinity to plus infinity. Other critical points are much better behaved. The y intercept is when x = 0 or 4/6 = 2/3. So the point is (0,2/3)
There is one x intercept at y = 0. When that happens
x + 4 = 0
x = - 4
Point (-4,0)
Notice the whole denominator gets multiplied out. 0 * (x + 6) = 0
1. The denominator gives a discontinuity point at (x = - 6). You can tell that is happening just by looking at the graph at x = - 6. The range at that point is - infinity to plus infinity. Other critical points are much better behaved. The y intercept is when x = 0 or 4/6 = 2/3. So the point is (0,2/3)
There is one x intercept at y = 0. When that happens
x + 4 = 0
x = - 4
Point (-4,0)
Notice the whole denominator gets multiplied out. 0 * (x + 6) = 0
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