Certainly! Let's work through the given problem step by step and find the values for the function \( f(x) = x^2 + 9x - 6 \) at specific points:
### Step-by-Step Solution:
1. Define the function:
[tex]\[
f(x) = x^2 + 9x - 6
\][/tex]
2. Calculate \( f(0) \):
Substitute \( x = 0 \) into the function:
[tex]\[
f(0) = 0^2 + 9 \times 0 - 6 = -6
\][/tex]
3. Calculate \( f(1) \):
Substitute \( x = 1 \) into the function:
[tex]\[
f(1) = 1^2 + 9 \times 1 - 6 = 1 + 9 - 6 = 4
\][/tex]
4. Calculate \( f(3) \):
Substitute \( x = 3 \) into the function:
[tex]\[
f(3) = 3^2 + 9 \times 3 - 6 = 9 + 27 - 6 = 30
\][/tex]
So, we have the following values:
[tex]\[
f(0) = -6, \quad f(1) = 4, \quad f(3) = 30
\][/tex]
These calculations give us the values of the function [tex]\( f(x) \)[/tex] at [tex]\( x = 0 \)[/tex], [tex]\( x = 1 \)[/tex], and [tex]\( x = 3 \)[/tex].
