Question

1. what is the y-intercepts of $f(x) = 1 + 7x + 9x^3 + 6x^4 - 2x^5$. how do you know?

Explanation:

Step1: Recall y-intercept definition

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

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

Given \( f(x)=1 + 7x+9x^{3}+6x^{4}-2x^{5} \), when \( x = 0 \), we have:
\( f(0)=1+7(0)+9(0)^{3}+6(0)^{4}-2(0)^{5} \)
Simplify each term: \( 7(0) = 0 \), \( 9(0)^{3}=0 \), \( 6(0)^{4}=0 \), \( - 2(0)^{5}=0 \).
So \( f(0)=1+0 + 0+0 - 0=1 \).

Answer:

The y - intercept of \( f(x) \) is \( 1 \). We know this because to find the y - intercept, we substitute \( x = 0 \) into the function, and after simplifying the terms with \( x \), we are left with the constant term \( 1 \).