Question

what is the y-intercept of the polynomial $f(x)$ defined below? write the y-value only. $f(x) = 2 - 3x^3 - 6x^5 - x^6$

Explanation:

Step1: Recall y-intercept definition

The y-intercept of a function \( f(x) \) is the value of \( f(x) \) when \( x = 0 \). So we substitute \( x = 0 \) into the polynomial \( f(x) \).

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

Given \( f(x)=2 - 3x^{3}-6x^{5}-x^{6} \), when \( x = 0 \), we have:
\( f(0)=2-3(0)^{3}-6(0)^{5}-(0)^{6} \)
Since any non - zero number raised to the power of 0 is 1, but 0 raised to any positive power is 0. So \( (0)^{3}=0 \), \( (0)^{5}=0 \), and \( (0)^{6}=0 \).
Then \( f(0)=2 - 0 - 0 - 0=2 \).

Answer:

2