1. ## polynomial graph

I have a question:

are all polynomial function has y-intercept and x-intercept?

2. No they don't.

Here's one without an x-intercept.

$f(x) = -x^2-5$

3. Originally Posted by pickslides
No they don't.

Here's one without an x-intercept.

$f(x) = -x^2-5$

that function looks like a linear. how about degree higher than 3?

4. Originally Posted by Anemori
that function looks like a linear.
It is not linear, it is quadratic. Are you aware of the differences?

Originally Posted by Anemori

My function has a y-intercept, you can find it by making $x=0$

Originally Posted by Anemori
how about degree higher than 3?
$g(x) = -x^4-5$

has order $> 3$ and no x-intercpets

5. Originally Posted by pickslides
It is not linear, it is quadratic. Are you aware of the differences?

My function has a y-intercept, you can find it by making $x=0$

$g(x) = -x^4-5$

has order $> 3$ and no x-intercpets

so in any polynomials y-intercept is always exist and x-intercept is not.

6. The y-intercept is where x= 0. Since evaluating a polynomial involves only multiplication and addition or subtraction, which are possible for any real number, the domain of a polynomial always includes all real numbers, including 0.

The x-intercept is where y, the value of the polynomial, is 0. Any polynomial of odd degree crosses the x-axis and so has an x-intercept. Polynomials of even degree may or may not have an x-intercept.

7. Originally Posted by HallsofIvy
The y-intercept is where x= 0. Since evaluating a polynomial involves only multiplication and addition or subtraction, which are possible for any real number, the domain of a polynomial always includes all real numbers, including 0.

The x-intercept is where y, the value of the polynomial, is 0. Any polynomial of odd degree crosses the x-axis and so has an x-intercept. Polynomials of even degree may or may not have an x-intercept.

Thanks for the explanation.

8. Originally Posted by HallsofIvy
The y-intercept is where x= 0. Since evaluating a polynomial involves only multiplication and addition or subtraction, which are possible for any real number, the domain of a polynomial always includes all real numbers, including 0.

The x-intercept is where y, the value of the polynomial, is 0. Any polynomial of odd degree crosses the x-axis and so has an x-intercept. Polynomials of even degree may or may not have an x-intercept.

Hello here is one Polynomial rational function problem that does not have y-intercept.

$g(x) = \frac {2x-1}{x^2}$

can you verify that please. thanks!

9. Originally Posted by Anemori
Hello here is one Polynomial rational function problem that does not have y-intercept.

$g(x) = \frac {2x-1}{x^2}$

can you verify that please. thanks!
true, it has an asymptote at $x=0$

10. Originally Posted by Anemori
Hello here is one Polynomial rational function problem that does not have y-intercept.

$g(x) = \frac {2x-1}{x^2}$

can you verify that please. thanks!
you're mixing functions.

polynomial functions are not rational functions.

polynomial functions have the form ...

$f(x) = ax^n + bx^{n-1} + cx^{n-2} + ... + dx + e
$

and are defined for all real x.