We are given the graph of a function $g(x)$ and are asked to find specific values of the function, both $g(x)$ for given $x$ values, and $x$ values for given $g(x)$ values.

1. Problem Description

We are given the graph of a function $g(x)$ and are asked to find specific values of the function, both $g(x)$ for given $x$ values, and $x$ values for given $g(x)$ values.

2. Solution Steps

a. To find $g(1)$, we locate $x=1$ on the x-axis and find the corresponding $y$ value on the graph. From the graph, we can see that $g(1) = 8$.

b. To find $g(4)$, we locate $x=4$ on the x-axis and find the corresponding $y$ value on the graph. From the graph, we can see that $g(4) = 5$.

c. We are given that $g(x) = \frac{15}{4} = 3.75$. We want to find the value of $x$ for which $g(x)$ is 3.

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5. Looking at the graph, we find that the $x$-value corresponding to $y=3.75$ is $x=5.25$.

d. We are given that $g(x) = 6$. We want to find the value of $x$ for which $g(x)$ is

6. Looking at the graph, we find that the $x$-value corresponding to $y=6$ is $x=3$.

3. Final Answer

a. $g(1) = 8$

b. $g(4) = 5$

c. $g(x) = \frac{15}{4}, x = 5.25$

d. $g(x) = 6, x = 3$