Question

find the y-coordinate of the y-intercept of the polynomial function defined below. \\( f(x) = 9x^3 - 9 - 2x^2 - 9x \\)

Explanation:

Step1: Recall y-intercept definition

The y - intercept of a function \( f(x) \) occurs where \( x = 0 \). So we need to find \( f(0) \).

Step2: Substitute \( x = 0 \) into \( f(x) \)

Given \( f(x)=9x^{3}-9 - 2x^{2}-9x \), substitute \( x = 0 \):
\( f(0)=9(0)^{3}-9-2(0)^{2}-9(0) \)

Step3: Simplify the expression

Simplify each term: \( 9(0)^{3}=0 \), \( - 2(0)^{2}=0 \), \( -9(0)=0 \). So \( f(0)=0 - 9-0 - 0=-9 \).

Answer:

\(-9\)