Where are the asymptotes for the following function located? f (x) = StartFraction 14 Over (x minus 5) (x + 1) EndFraction
1 answer:
Answer:
2 vertical asymptotes occurring at x = 5 and x = -1
Step-by-step explanation:
given
recall that asymptotic occur at the locations that will make the equation undefined. In this case, the asymptote will occur at x-locations which will cause the denominator to become zero (and hence undefined)
Equating the denominator to zero,
(x-5)(x+1) = 0
(x-5) =0
x = 5 (first asymptote)
or (x+1) = 0
x = -1 (2nd asymptote)
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Answer:
To graph (like the provided picture) you must understand y=mx+b. Your m would stand for your slope which you need to determine with rise over run. Rise over run can be done by finding a place where both the x and y values are lined up. (0,-2) can be used as an example from the picture. You then want to find the next point where the x and y values line up which (-2,1) can be used. Go up 3 units and go to the LEFT 2 times which makes this a negative run. The slope would then be represented as -3/2.
Your x value stands for your x-value moving up or down while you b value stands for your y-intercept which point (0,-2) is represented as. Y represents the y value after the equation is plugged in with x and solved.
