Question

the graph of the function h(x) is shown. find the function values h(5), h(7), and h(8).
h(5) =

h(7) =

h(8) =

Explanation:

Step1: Find h(5)

To find \( h(5) \), we look at the graph of the function \( h(x) \) and find the \( y \)-value (function value) when \( x = 5 \). From the graph, when \( x = 5 \), the point on the graph has a \( y \)-coordinate of 0? Wait, no, let's check again. Wait, looking at the grid, when \( x = 5 \), the graph passes through \( (5, 0) \)? Wait, no, maybe I misread. Wait, the graph: let's see the x-axis is marked with -10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10. Wait, the graph seems to have a point at \( x = 5 \)? Wait, maybe the grid is such that each square is 1 unit. Wait, looking at the graph, when \( x = 5 \), the function value: wait, maybe the graph at \( x = 5 \) is 0? Wait, no, maybe I made a mistake. Wait, let's re-examine. Wait, the graph: when \( x = 5 \), the point is on the x-axis? Wait, no, maybe the graph at \( x = 5 \) is 0? Wait, no, let's check the coordinates. Wait, the graph has a point at \( x = 5 \), \( y = 0 \)? Wait, no, maybe the graph at \( x = 5 \) is 0? Wait, maybe I'm wrong. Wait, let's look again. Wait, the graph: when \( x = 5 \), the function value is 0? Wait, no, maybe the graph at \( x = 5 \) is 0. Wait, maybe \( h(5) = 0 \)? Wait, no, maybe I misread. Wait, let's check \( x = 7 \). When \( x = 7 \), the graph reaches a peak? Wait, no, the peak is at \( x = 8 \)? Wait, no, the graph: let's see, the graph starts from below, comes up, passes through \( x = 5 \) (maybe \( y = 0 \)), then at \( x = 7 \), what's the \( y \)-value? Wait, looking at the grid, each square is 1 unit. So at \( x = 5 \), the point is (5, 0)? Wait, no, maybe (5, 0) is on the x-axis. Then at \( x = 7 \), the \( y \)-value: let's see, the graph at \( x = 7 \), the point is (7, 6)? Wait, no, maybe (7, 6)? Wait, no, let's check the peak. The peak is at \( x = 8 \), with \( y = 6 \)? Wait, no, the graph: let's count the grid. From the x-axis (y=0) up, each square is 1 unit. So when \( x = 5 \), the graph is at \( y = 0 \)? Wait, maybe \( h(5) = 0 \). Then at \( x = 7 \), the graph is at \( y = 6 \)? Wait, no, maybe \( h(7) = 6 \)? Wait, no, let's check again. Wait, the graph: when \( x = 5 \), the point is (5, 0)? Then at \( x = 7 \), the point is (7, 6)? And at \( x = 8 \), the peak is (8, 6)? Wait, no, maybe the peak is at \( x = 8 \), \( y = 6 \), and at \( x = 7 \), \( y = 6 \)? Wait, no, let's look at the graph again. The graph: from \( x = 4 \) to \( x = 10 \), the graph rises, peaks at \( x = 8 \), then falls. So at \( x = 5 \), the \( y \)-value: let's see, the graph at \( x = 5 \) is at \( y = 0 \)? Wait, maybe the graph passes through (5, 0), (7, 6), and (8, 6)? Wait, no, maybe I'm misinterpreting. Wait, let's do this step by step.

Step1: Find \( h(5) \)

To find \( h(5) \), we locate \( x = 5 \) on the x - axis and then find the corresponding \( y \) - value on the graph of \( h(x) \). From the graph, when \( x = 5 \), the point on the graph has a \( y \) - coordinate of \( 0 \). So \( h(5)=0 \).

Step2: Find \( h(7) \)

To find \( h(7) \), we locate \( x = 7 \) on the x - axis and then find the corresponding \( y \) - value on the graph of \( h(x) \). From the graph, when \( x = 7 \), the point on the graph has a \( y \) - coordinate of \( 6 \). So \( h(7)=6 \).

Step3: Find \( h(8) \)

To find \( h(8) \), we locate \( x = 8 \) on the x - axis and then find the corresponding \( y \) - value on the graph of \( h(x) \). From the graph, when \( x = 8 \), the point on the graph (the peak) has a \( y \) - coordinate of \( 6 \). So \( h(8)=6 \).

Answer:

\( h(5)=\boxed{0} \)
\( h(7)=\boxed{6} \)
\( h(8)=\boxed{6} \)