Question

use the graph below to answer the following question. the graph represents the function g(x). find g(2).

Explanation:

Step1: Understand the problem

We need to find the value of \( g(2) \) from the graph of the function \( g(x) \). This means we look for the \( y \)-value (output) when \( x = 2 \) (input) on the graph.

Step2: Locate \( x = 2 \) on the x - axis

Find the point on the graph where the \( x \)-coordinate is 2. Then, determine the corresponding \( y \)-coordinate of that point. From the graph (assuming the grid and the line's behavior), when we move to \( x = 2 \) on the x - axis and then find the point on the graph of \( g(x) \) at that \( x \)-value, we can see the \( y \)-value. Looking at the graph's structure (the left - hand line before the vertex), we can analyze the slope or the pattern. Let's assume the left - hand line has a slope. Let's take two points on the left - hand line, for example, when \( x = 0 \), from the graph, we can see that the \( y \)-value (let's call it \( g(0) \)) is 5? Wait, no, looking at the graph, when \( x = 0 \), the point is at \( y = 5 \)? Wait, no, the original graph: let's re - examine. Wait, the left - hand line: when \( x = 0 \), the \( y \)-coordinate is 5? Wait, no, the user's graph: the left line goes from the top left, passes through \( (0,5) \)? Wait, no, the problem's graph: the left part of the graph (before the vertex) is a line. Let's find the equation of the left - hand line. Let's take two points: suppose when \( x = 0 \), \( y = 5 \) (wait, no, the graph has a point at \( x = 0 \) with \( y = 5 \)? Wait, no, the options are 1,3,2,0,4. Wait, maybe the left - hand line has a slope. Let's consider that when \( x = 0 \), \( g(0)=5 \)? No, maybe I made a mistake. Wait, the vertex is at \( x = 5 \) (maybe). Wait, no, the x - axis has marks at 0,5,10. Wait, the left line: let's see, when \( x = 0 \), the \( y \)-value is 5? Wait, no, the problem is to find \( g(2) \). Let's think about the graph's structure. The left - hand line (before the vertex) is a straight line. Let's assume that the left - hand line passes through \( (0,5) \) and let's say another point. Wait, maybe the slope of the left - hand line is \( m=\frac{y_2 - y_1}{x_2 - x_1}\). Suppose when \( x = 5 \), the vertex is at \( y = 0 \) (the bottom of the V - shape). Wait, no, the vertex is at \( x = 5 \) with \( y = 0 \)? Wait, no, the graph's vertex seems to be at \( x = 5 \) (the middle of the x - axis marks 0,5,10) and \( y = 0 \). Then the left - hand line goes from the top left to \( (5,0) \). Let's find the equation of the left - hand line. Let's take two points: let's say when \( x = 0 \), \( y = 5 \) (since from \( (5,0) \) to \( (0,5) \), the slope \( m=\frac{0 - 5}{5 - 0}=\frac{- 5}{5}=- 1 \)). So the equation of the left - hand line is \( y-0=-1(x - 5) \), which simplifies to \( y=-x + 5 \). Now, when \( x = 2 \), we substitute \( x = 2 \) into the equation \( y=-x + 5 \). So \( y=-2 + 5=3 \).

Answer:

B. 3