Write x^4+4x^3+5x^3-20x-40 ÷ x^2-5
1 answer:
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Answer:
x=-2.5 if the function is
Step-by-step explanation:
has discontinuities when the denominator is 0.
You will either have a hole or a vertical asymptote depending on what happens to the numerator after you find when the bottom is 0.
That is whatever you found that makes the bottom 0, if it makes the top also 0 then you will have a hole at x=the number that made the bottom 0.
If it makes the top anything other than 0, then it is a vertical asymptote at x=the number you found that made the bottom 0.
Let's do this now.
When is -4x-10 equal to 0?
We have to solve the equation:
-4x-10=0
Add 10 on both sides:
-4x=10
Divide both sides by -4:
x=10/-4
Reduce by dividing top and bottom by 2:
x=5/-2
x=-5/2
or
x=-2.5 (if you want decimal form)
Now does it make the top 0? This is the deciding factor on whether you have a hole at x=-2.5 or a vertical asymptote at x=-2.5.
Let's see.
8(-2.5)-3=-23
Since the top is not 0 at x=-2.5 then you have a vertical asymptote at x=-2.5.
If the top were 0, then you would have had a hole at x=-2.5.
The single dilation of the shape is a dilation by a scale factor of 1.5 with center R
<h3>How to determine the dilation rule?</h3>From the graph, we have the center of dilation to be point R.
This is so because R = R'
Also, we have:
R = (-1, -4)
S = (2, 0)
S' = (3.5, 2)
Calculate the distance RS and RS' using
This gives
Divide RS' by RS to determine the scale factor (k)
k = 7.5/5
k = 1.5
Hence, the single dilation of the shape is a dilation by a scale factor of 1.5 across point R
Read more about dilation at:
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