Question

function g is represented by the graph.
for what input value or values is g(x) = 4?
2
-2 and 2
16
none

Explanation:

Step1: Understand the problem

We need to find the input values (x - values) for which \( g(x)=4 \). This means we look for the points on the graph of function \( g \) where the \( y \) - coordinate is 4, and then find the corresponding \( x \) - coordinates.

Step2: Analyze the graph

The graph of function \( g \) is a parabola opening upwards with vertex at the origin \((0,0)\). We draw a horizontal line \( y = 4 \) (since we want to find where \( g(x)=4\), i.e., \( y = 4\)) and see where this line intersects the parabola.

Looking at the grid, when \( y = 4 \), we can see that the horizontal line \( y = 4 \) intersects the parabola at two points. To find the \( x \) - coordinates of these intersection points, we look at the \( x \) - axis.

From the symmetry of the parabola (it is symmetric about the \( y \) - axis), we can observe that when \( y = 4 \), the \( x \) - values are \( x=- 2 \) and \( x = 2 \). Because for a parabola symmetric about the \( y \) - axis, if \((x,y)\) is on the parabola, then \((-x,y)\) is also on the parabola. When \( y = 4 \), we can see that the points of intersection have \( x\) - values of \(-2\) and \(2\).

Answer:

-2 and 2 (corresponding to the option: -2 and 2)