Questions: Polynomial and Rational Functions Finding x - and y-intercepts given a polynomial function Find all x-intercepts and y-intercepts of the graph of the function. f(x)=x^3-3 x^2-x+3 If there is more than one answer, separate them with commas. Click on "None" if applicable. x-intercept(s): None √ √[]

Polynomial and Rational Functions
Finding x - and y-intercepts given a polynomial function

Find all x-intercepts and y-intercepts of the graph of the function.

f(x)=x^3-3 x^2-x+3

If there is more than one answer, separate them with commas.
Click on "None" if applicable.
x-intercept(s):
None
√
√[]

Transcript text: Polynomial and Rational Functions Finding $x$ - and $y$-intercepts given a polynomial function Find all $x$-intercepts and $y$-intercepts of the graph of the function. \[ f(x)=x^{3}-3 x^{2}-x+3 \] If there is more than one answer, separate them with commas. Click on "None" if applicable. $x$-intercept(s): $\square$ None $\sqrt{\square}$ $\sqrt[\square]{\square}$ $\square$

Solution

Solution Steps

Step 1: Finding the y-intercept

To find the y-intercept of the polynomial, we substitute $x = 0$ into the polynomial function. This gives us the y-intercept as $f(0) = 3$.

Step 2: Finding the x-intercepts

For polynomials of degree greater than 2, we find the roots of the polynomial equation. The real roots correspond to the x-intercepts of the graph. This gives us the x-intercepts at $x = [3, -1, 1]$.