Graph the function:
Find the x and y intercepts, vertical asymptotes, horizontal asymptotes if there are any.
To find the x-intercept you have to plug zero in for y and the only way the function can equal zero is if the numerator equals zero.
Your x-intercept equals -5.
To get the y-intercept you plug zero into x.
The y-intercept equals -7.5
To find the vertical asymptote you have to find out what makes the functions undefinded which is when the denominator equals zero.
The vertical asymptote is
Finding the horizontal asymptote has to do with the highest power factor and there are three different ways of finding it:
1. If the numerator's highest power is higher than the denominator's then there is no horizontal asymptote.
2. If the numerator and denominator's highest powers are equal than it is the leading coefficients of the highest power over each other:
This H.A is 2
3. If the denminator's highest power is higher then the numerator than the horizontal asymptote is y=0
This problems equation has equal powers so the horizontal asymptote is y=3.
The graph:
There is one exception about vertical asymptotes and it is if you plug that number in the top and both the top and bottom then there is a hole in the graph instead of a line.
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