Question

the graph a function ( f ) is shown.

for what value of ( x ) is ( f(x) = 0 )?

( x = square )

Explanation:

Step1: Understand the problem

We need to find the value of \( x \) where \( f(x) = 0 \). This means we are looking for the \( x \)-intercept of the function \( f \), which is the point where the graph of the function crosses the \( x \)-axis (where \( y = 0 \)).

Step2: Analyze the graph

Looking at the given graph of the function \( f \), we observe the line (since it's a linear function) and find the point where it intersects the \( x \)-axis. From the graph, we can see that the line crosses the \( x \)-axis at \( x = 3 \). To confirm, we can also find the equation of the line. Let's find the slope first. The line passes through \( (0, -2) \) (the \( y \)-intercept) and another point, say \( (3, 0) \) (the \( x \)-intercept we think). The slope \( m \) is calculated as \( m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{0 - (-2)}{3 - 0}=\frac{2}{3} \). The equation of the line is \( y=\frac{2}{3}x - 2 \). To find when \( y = 0 \), we set \( 0=\frac{2}{3}x - 2 \). Solving for \( x \):
\[

$$\begin{align*} \frac{2}{3}x - 2&=0\\ \frac{2}{3}x&=2\\ x&=2\times\frac{3}{2}\\ x&= 3 \end{align*}$$

\]

Answer:

\( 3 \)