Use the graph of g to solve Exercises 71–76.

For what value of x is g(x) = -1?

Verified step by step guidance

1. Observe the graph of the function g(x) and identify the horizontal line y = -1, which represents the value of g(x) = -1.
2. Determine the x-coordinates where the graph of g(x) intersects the horizontal line y = -1. These x-coordinates are the solutions to the equation g(x) = -1.
3. From the graph, locate the points of intersection between the graph of g(x) and the line y = -1. Carefully read the x-coordinates of these points.
4. Verify that the identified x-coordinates correspond to the points where the graph of g(x) has a y-value of -1.
5. List the x-values where g(x) = -1 as the solution to the problem.

Key Concepts

Function Graphs

A function graph visually represents the relationship between input values (x) and output values (g(x)). Each point on the graph corresponds to a specific x-value and its associated g(x) value, allowing us to see how the function behaves across its domain.

Finding Function Values

To find the value of x for which g(x) equals a specific number, such as -1, we look for the points on the graph where the output (y-value) intersects with that number. This involves identifying the x-coordinates at which the function reaches the desired output.

Intercepts

Intercepts are points where the graph crosses the axes. The x-intercept occurs where g(x) = 0, while the y-intercept occurs where x = 0. Understanding intercepts helps in analyzing the function's behavior and can provide insights into its roots and overall shape.