Question

A parabola and a dotted straight line are drawn on a coordinate plane. The x-axis ranges from negative 5 to 10 in one-unit increments and the y-axis ranges from 0 to 15 in one-unit increments.
The graph of g(x)
and f(x)
is shown. What is the smaller solution to g(x)=f(x)
?

(1 point)
Responses

6
6

13
13

3
3

1
1

Answer 1

To determine the smaller solution to the equation \( g(x) = f(x) \), we need to analyze the intersection points of the parabola \( g(x) \) and the line \( f(x) \) on the given coordinate plane.

The smaller solution occurs at the leftmost intersection point where the values of \( g(x) \) and \( f(x) \) are equal. Based on the options given, we are looking for one of the following values:

- 6
- 13
- 3
- 1

Without the specific graphs, we make some logical deductions based on common behaviors of parabolas and lines. Typically, a parabola opens upwards or downwards, while a straight line can be presented in various slopes.

To find the smaller solution:
1. Consider each of the response numbers (1, 3, 6, 13) and visually or analytically assess where the curves intersect.
2. Since we are looking for the smaller solution, we will check the lower values first.

If you had the graph handy, you would look for where the graph of \( g(x) \) crosses \( f(x) \) and identify which of these specified x-values corresponds to the smaller intersection.

If the parabola and straight line revealed that they intersect at x = 1, x = 3, and so on, we would select the smallest.

Thus, without additional details, if the smaller solution appears to be x = 1 based on typical intersections of graphs, we would choose:

**1** as the answer, pending confirmation from the graph context provided in your question.