Question: Refer to the graph of \( y = g(x) \) shown to the right. Find \( g(-5) \), \( g(1) \), and…

Refer to the graph of \( y = g(x) \) shown to the right. Find \( g(-5) \), \( g(1) \), and \( g(3) \).

What is the value of \( g(-5) \)?

What is the value of \( g(1) \)?

What is the value of \( g(3) \)?

[Graph of \( y = g(x) \) is shown with points plotted at (-5, -4), (1, 2), and (3, 6).]

Solution

To find the values of \( g(-5) \), \( g(1) \), and \( g(3) \), we will look at the graph of \( y = g(x) \). 1. Find \( g(-5) \): Check the graph at \( x = -5 \). The point on the graph corresponding to \( x = -5 \) is at \( y = -2 \). So, \( g(-5) = -2 \). 2. Find \( g(1) \): Check the graph at \( x = 1 \). The point on the graph corresponding to \( x = 1 \) is at \( y = 4 \). So, \( g(1) = 4 \). 3. Find \( g(3) \): Check the graph at \( x = 3 \). The point on the graph corresponding to \( x = 3 \) is at \( y = 2 \). So, \( g(3) = 2 \). Thus, the values are: \[ \begin{cases} g(-5) = -2 & \\ g(1) = 4 & \\ g(3) = 2 & \end{cases} \]