Question

question
find $g(1)$.
(there is a graph of the function $g(x)$ here, showing a parabola on a coordinate plane with x-axis from -10 to 10 and y-axis from -10 to 10.)
answer

Explanation:

Step1: Understand the task

We need to find the value of \( g(1) \) from the graph of the function \( g(x) \). This means we need to determine the \( y \)-coordinate of the point on the graph where \( x = 1 \).

Step2: Locate \( x = 1 \) on the x - axis

On the given graph, find the vertical line corresponding to \( x = 1 \). This is a vertical line passing through the point \( (1,0) \) on the x - axis.

Step3: Find the intersection with the graph

Now, find the point where this vertical line \( x = 1 \) intersects the graph of \( g(x) \). Then, determine the \( y \)-coordinate of this intersection point. From the graph, when we move up from \( x = 1 \) on the x - axis until we meet the graph of \( g(x) \), we can see that the \( y \)-coordinate at \( x = 1 \) is \( 0 \)? Wait, no, wait. Wait, let's re - examine the graph. Wait, the graph is a parabola. Let's check the coordinates again. Wait, when \( x = 0 \), the \( y \)-intercept is \( 4 \)? Wait, no, looking at the graph, the parabola crosses the y - axis at \( (0,4) \)? Wait, no, maybe I made a mistake. Wait, let's look at the grid. Each square is 1 unit. Let's find \( x = 1 \). The vertical line \( x = 1 \) intersects the graph. Let's see, the graph crosses the x - axis at \( x=-3 \) and \( x = 1 \)? Wait, no, the roots: when \( y = 0 \), the x - intercepts. Wait, the graph of \( g(x) \) intersects the x - axis at \( x=-3 \) and \( x = 1 \)? Wait, no, if we look at the graph, when \( x = 1 \), the point on the graph is on the x - axis? Wait, no, maybe I misread. Wait, let's check again. The parabola: the vertex is at \( x=-1 \), \( y = 5 \). Then, when \( x = 0 \), \( y = 4 \)? Wait, no, the y - intercept is at \( (0,4) \)? Wait, no, the graph as drawn: let's count the grid. From \( x = 0 \), moving to \( x = 1 \), the graph goes from \( (0,4) \) down to \( (1,0) \)? Wait, yes, because the parabola crosses the x - axis at \( x=-3 \) and \( x = 1 \). So when \( x = 1 \), the \( y \)-coordinate is \( 0 \)? Wait, no, wait, if the x - intercepts are at \( x=-3 \) and \( x = 1 \), then \( g(1)=0 \). Wait, but let's confirm. The function \( g(x) \) at \( x = 1 \): we look at the graph, find \( x = 1 \) on the x - axis, go up (or down) to the graph. The graph passes through \( (1,0) \), so \( g(1)=0 \).

Wait, maybe I made a mistake earlier. Let's re - check. The graph of \( g(x) \): when \( x = 1 \), the point is on the x - axis, so \( y = 0 \). So \( g(1)=0 \).

Answer:

\( 0 \)