Chewbacka2020
29.07.2019 •
Mathematics
What is the discontinuity and zero of the function f(x)= 3x^2+x-4/x-1
a) discontinuity at (-1,1), zero at (4/3,0)
b) discontinuity at (-1,1), zero at (-4/3,0)
c)discontinuity at (1,7), zero at (4/3,0)
d)discontinuity at (1,7), zero at (-4/3, 0)
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Ответ:
D.
Step-by-step explanation:
To find the discontinuity given this is a fraction, we only have to worry about dividing by 0.
So we only have to worry about x-1 being 0.
x-1=0
Add 1 on both sides gives:
x=1
So there is a discontinuity when x=1.
Now there cannot also be a zero at this number since the function doesn't exist there.
However if you plug 1 into the fraction before simplification any you get 0/0 then you have a hole at x=1.
.
So we do indeed have a hole at x=1.
To find point that would make this function continuous at x=1, we will simplify our fraction and then plug in 1:
I already know x-1 is a factor of the top because x=1 made it zero on top:
The (x-1)'s cancel:
Now 3x+4 evaluated at x=1 gives 3(1)+4=3+4=7.
So the hole is at (1,7).
The choice is either C or D.
The zero is when 3x+4 is 0.
This is the numerator after simplification. The top of the fraction is what determines if the fraction itself will be 0 since 0/anything is 0 except when you are dividing by 0.
3x+4=0
Subtract 4 on both sides gives:
3x=-4
Divide both sides by 3:
x=-4/3
So the zero is at (-4/3,0).
Ответ:
4.
Step-by-step explanation:
The slope = (difference in y coordinates) / (corresponding difference in the x coordinates)
= (10-6)/ (2-1)
= 4 / 1
= 4.