Question

the piecewise function h(x) is shown on the graph. what is the value of h(3)? -2 -1 1 2

Explanation:

Step1: Locate x = 3 on the graph

Find the vertical line corresponding to \( x = 3 \) on the coordinate plane.

Step2: Find the y - value at x = 3

Look at the point on the graph of \( h(x) \) where \( x = 3 \). The graph at \( x = 3 \) is part of the line segment. By observing the grid, when \( x = 3 \), the \( y \) - coordinate (which is \( h(3) \)) can be determined. The line from \( (1,3) \) to \( (4,0) \) has a slope, but we can directly read the value. At \( x = 3 \), moving up from \( x = 3 \) on the x - axis, the point on the graph has a \( y \) - value of 1? Wait, no, let's re - examine. Wait, the line goes from (1,3) to (4,0). The equation of the line: the slope \( m=\frac{0 - 3}{4 - 1}=\frac{- 3}{3}=-1 \). Using point - slope form \( y - y_1=m(x - x_1) \), with \( (x_1,y_1)=(1,3) \), we get \( y-3=-1(x - 1) \), so \( y=-x + 4 \). When \( x = 3 \), \( y=-3 + 4 = 1 \). Wait, but let's check the graph again. The grid: each square is 1 unit. At \( x = 3 \), the point on the graph is at \( y = 1 \)? Wait, no, maybe I made a mistake. Wait, the horizontal line is at \( y = 3 \) from \( x=-1 \) (closed dot) to \( x = 1 \) (closed dot), then a line from \( (1,3) \) to \( (4,0) \). So when \( x = 3 \), plug into \( y=-x + 4 \), \( y=-3 + 4=1 \). So \( h(3)=1 \)? Wait, but let's check the options. The options are - 2, - 1, 1, 2. So the value of \( h(3) \) is 1.

Answer:

1