Respuesta :
Answer:
A, B, and E
if I read your functions right.
Step-by-step explanation:
It's zeros are x=-6,-2, and 2.
This means we want the factors (x+6) and (x+2) and (x-2) in the numerator.
It has a y-intercept of 4. This means we want to get 4 when we plug in 0 for x.
And it's long-run behavior is y approaches - infinity as x approaches either infinity. This means the degree will be even and the coefficient of the leading term needs to be negative.
So let's see which functions qualify:
A) The degree is 4 because when you do x^2*x*x you get x^4.
The leading coefficient is -4/144 which is negative.
We do have the factors (x+6), (x+2), and (x-2).
What do we get when plug in 0 for x:
[tex]\frac{-4}{144}(0+6)^2(0+2)(0-2)[/tex]
Put into calculator: 4
A works!
B) The degree is 6 because when you do x*x^4*x=x^6.
The leading coefficient is -4/192 which is negative.
We do have factors (x+6), (x+2), and (x-2).
What do we get when we plug in 0 for x:
[tex]\frac{-4}{192}(0+6)(0+2)^4(x-2)[/tex]
Put into calculator: 4
B works!
C) The degree is 4 because when you do x*x*x*x=x^4.
The leading coefficient is -4 which is negative.
Oops! It has a zero at 0 because of that factor of (x) between -4 and (x+6).
So C doesn't work.
D) The degree is 3 because x*x*x=x^3.
We needed an even degree.
D doesn't work.
E) The degree is 4 because x*x^2*x=x^4.
The leading coefficient is -4/48 which is negative.
It does have the factors (x+6), (x+2), and (x-2).
What do we get when we plug in 0 for x:
[tex]\frac{-4}{48}(0+6)(0+2)^2(0-2)[/tex]
Put into calculator: 4
So E does work.
F) The degree is 4 because x*x*x^2=x^4.
The leading coefficient is -4/48.
It does have factors (x+6), (x+2), and (x-2).
What do we get when we plug in 0 for x:
[tex]\frac{-4}{48}(0+6)(0+2)(0-2)^2[/tex]
Put into calculator: -4
So F doesn't work.
G. I'm not going to go any further. The leading coefficient is 4/48 and that is not negative.
So G doesn't work.
Answer:
D. [tex]y=-\frac{4}{24} (x+6)(x+2)(x-2)[/tex]
Step-by-step explanation:
Notice that we have 3 zeros, which means there are only 3 roots, which are -6, -2 and 2, this indicates that our expression must be cubic with the binomials (x+6), (x+2) and (x-2).
We this analysis, possible choices are C and D.
Now, according to the problem, it has y-intercept at y = 4, so let's evaluate each expression for x = 0.
C.
[tex]y=-4x(x+6)(x+2)(x-2)\\y=-4(0)(0+6)(0+2)(0-2)\\y=0[/tex]
D.
[tex]y=-\frac{4}{24} (x+6)(x+2)(x-2)\\y=-\frac{4}{24}(0+6)(0+2)(0-2)\\y=-\frac{4}{24}(-24)\\ y=4[/tex]
Therefore, choice D is the right expression because it has all given characteristics.
