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 2. So, \( h(5)=2 \).

Step2: Find h(7)

To find \( h(7) \), we look at the graph of the function \( h(x) \) and find the \( y \)-value when \( x = 7 \). From the graph, the vertex (highest point) of the graph is at \( x = 7 \), and the \( y \)-coordinate at this point is 6. So, \( h(7)=6 \).

Step3: Find h(8)

To find \( h(8) \), we look at the graph of the function \( h(x) \) and find the \( y \)-value when \( x = 8 \). From the graph, when \( x = 8 \), the \( y \)-coordinate of the point on the graph is 2 (since the graph is symmetric around \( x = 7 \), the value at \( x = 8 \) should be the same as at \( x = 6 \), and from the graph, we can see it's 2). So, \( h(8)=2 \).

Answer:

\( h(5)=\boxed{2} \)
\( h(7)=\boxed{6} \)
\( h(8)=\boxed{2} \)