can the graph of a polynomial function have no y-intercept?

Answer 1

Of course not. ALL polynomial functions have a y-intercept.

All polynomial functions are of the form

f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0

where, and here's the important one, n > 0 and belongs to NATURALS. Not *integers*. So 1/x is NOT polynomial, shame on you Nick :)

Since all the exponents are natural, there is no reason why f(0) would not exist. It would -- it is exactly equal to a_0. So every polynomial function does have exactly one y-intercept, and it is equal to the constant term. QED.

Answer 2

No, it is not possible if the function is a polynomial. Make sure you know that the function is a polynomial before you make that judgement, though. A good definition of "polynomial" is here:
http://en.wikipedia.org/wiki/Polynomial
Another note: It is possible for a polynomial to have no x-intercept if and only if the degree of the polynomial is even or zero (constant function). Again, make sure it is a polynomial before you make that judgement.
Good luck!
Edit: OK, I see one restriction that I should have established in my answer: The polynomials I was talking about were single-variable functions in terms of an independent variable x that are graphed in the conventional manner with y being the dependent variable. If the polynomial describes any other type of function (with y independent and x dependent, for example) or a function with dimension > 2, then the explanation above does not hold. I do not think that is what you thought of in asking the question, however, so just ignore the rest of it my answer unless you can understand it.

Answer 3

No, every polynomial function (in the variable x) will have exactly one y-intercept. (You just replace x with zero to find it.) The domain of a polynomial is all real numbers. Thus, zero is in the domain, so you will always be able to replace x with 0 to find the y-intercept.
It is possible to not have an x-intercept.
P(x) = x^2 + 1 does not have an x-intercept.
Note: x = 5 (or any other number) is not a polynomial function.
Also, note that y = 1/x is not a polynomial. Exponential functions are not polynomials (they are exponential functions) and square root equations are also not polynomials.

Answer 4

The graph of a polynomial function intercepts the y-axis always.
Then always x=0.

Answer 5

ok...is it possible yes...now, this depends what you want to call a polynomial...i claim that x=5 is a monomial...not a polynomial, and this graph would not intersect the y-axis, its a vertical line at x=5

now, your question is if a multiple termed function ould be created so that it doesnt cross the y-axis...and the answer is yes...heres why

for there to be no y-intercept then there can be a y value when x = 0

this would occur anytime you have an x in the denominator (the x could be to any power

so an example would be : y= (52x)/x^2 +5x

Answer 6

Of course not. ALL polynomial functions have a y-intercept.

All polynomial functions are of the form

f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0

where, and here's the important one, n > 0 and belongs to NATURALS. Not *integers*. So 1/x is NOT polynomial, shame on you Nick :)

Since all the exponents are natural, there is no reason why f(0) would not exist. It would -- it is exactly equal to a_0. So every polynomial function does have exactly one y-intercept, and it is equal to the constant term. QED.

Answer 7

All polynomials have y intercepts. don't let y= 1/x^2 fool you either. Equations simplified with x's to the negative powers are not polynomials.

Answer 8

no
Take any polynomial function
Ax^n +Bx^(n-1) +... Cx + D
The y-intercept(the line x=0) will be D

Also a polynomial function will also intercept every vertical line

NOTE- polynomial function are when n= 0,1,2,3,...
y =x^(1/2)
y =x^(-1) are not polynomial functions

Answer 9

Try y = 1/x. There is no x intercept nor y intercept. Also, x + 0y = 5 is not a function, vertical line test.

Answer 10

yes it can..but not in every case.

i believe y=mx + c (the general slope-intercept equation of a line) is a polynomial, ,which can also be expressed as x/a + y/b = c; it does have a y-intercept = b.