What is the y-intercept of the polynomial f, of, xf(x) defined below? Write the y-value only.

Question

f, of, x, equals, x, to the power 6 , minus, 2, x, to the power 7 , plus, 3, x, plus, 3, plus, 6, x, cubed
f(x)=x 6−2x7 +3x+3+6x3

Answer 1

The y-intercept of a polynomial is found by evaluating the function at \( x = 0 \).

Given the polynomial:

\[ f(x) = x^6 - 2x^7 + 3x + 3 + 6x^3 \]

Evaluating at \( x = 0 \):

\[ f(0) = (0)^6 - 2(0)^7 + 3(0) + 3 + 6(0)^3 = 0 - 0 + 0 + 3 + 0 = 3 \]

Therefore, the y-intercept of the polynomial is:

3