During his vacation, Dalyn rents a small boat from a rental service that charges a flat fee of $30 plus $10 per hour (including
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We must recall that a horizontal asymptote is the value/s of y that the given function approaches to but never reaches. To find this in a rational function, we compare the expressions with highest degree in the numerator and denominator. There are three possible outcome when this happens.
1. if the highest degree (highest exponent) in the numerator is bigger than that of the denominator, then there won't be any horizontal asymptote.
2. if the highest degree in the denominator is bigger, then the horizontal symptote would be y = 0.
3. if they have the same highest degree, then we just get the quotient of their coefficient.
Now, going back to our function, we have
From this we can see that the highest degree in the numerator is 1 (from 2x) and 2 (from x²) for the denominator. Clearly, it shows that its denominator has a higher degree. And from our discussion, we can conclude that the horizontal asymptote would be y = 0.
Answer: y = 0
1. if the highest degree (highest exponent) in the numerator is bigger than that of the denominator, then there won't be any horizontal asymptote.
2. if the highest degree in the denominator is bigger, then the horizontal symptote would be y = 0.
3. if they have the same highest degree, then we just get the quotient of their coefficient.
Now, going back to our function, we have
From this we can see that the highest degree in the numerator is 1 (from 2x) and 2 (from x²) for the denominator. Clearly, it shows that its denominator has a higher degree. And from our discussion, we can conclude that the horizontal asymptote would be y = 0.
Answer: y = 0
So, you can do this one of two ways.
The first is knowing what the numbers in your equation represent:
For example: y=mx+b in this case "b" is 9. b is the y-value when x=0. So the first point on our graph is (0,9). Next we have to pick an xvalue to solve for another y-coordinate.
I chose x= -3. Plug x into the equation to get y.
y=3x+9
y=3(-3)+9
y=(-9)+9
y=0
So, our second point is (-3,0).
connect the points with a ruler to graph the line.
The first is knowing what the numbers in your equation represent:
For example: y=mx+b in this case "b" is 9. b is the y-value when x=0. So the first point on our graph is (0,9). Next we have to pick an xvalue to solve for another y-coordinate.
I chose x= -3. Plug x into the equation to get y.
y=3x+9
y=3(-3)+9
y=(-9)+9
y=0
So, our second point is (-3,0).
connect the points with a ruler to graph the line.