Question

(b) For the functions from part (a) that do have 3 in their domain, find f(x)=x^(2)-3x

Answer 1

For the functions in part (a) with 3 in their domain, the expression
`\(f(x) = x^2 - 3x\)` evaluates to \(f(3) = 0\).

Step-by-step explanation:

The given expression
`\(f(x) = x^2 - 3x\)` represents a quadratic function. To find \(f(3)\), substitute \(x = 3\) into the expression:

`\[f(3) = (3)^2 - 3(3)\]`

Simplifying this, we get:

`\[f(3) = 9 - 9 = 0\]`

Therefore, the final answer is \(f(3) = 0\). This means that when \(x\) is equal to 3, the function value is zero. In the context of functions with 3 in their domain, this implies that the point \((3, 0)\) lies on the graph of these functions.

This result is significant because it provides a specific point of intersection with the x-axis. In graphical terms, it means that the function crosses the x-axis at \(x = 3\), indicating that 3 is a root or zero of the function. It's a crucial point on the graph where the function value becomes zero, and understanding such points helps in analyzing the behavior and properties of the function, contributing to a comprehensive understanding of its characteristics.