Question

A part of an exponential function is graphed on the grid. Which inequality best represents the domain of the part shown?

Answer 1

The inequality
`\(x \geq a\)`, where \(a\) is the x-coordinate of the leftmost point on the graph, best represents the domain of the part of the exponential function shown.

Step-by-step explanation:

When determining the domain of an exponential function from its graph, we look for the leftmost point on the x-axis where the graph starts. Let's denote this x-coordinate as \(a\). The exponential function is defined for all values of \(x\) greater than or equal to \(a\). Therefore, the appropriate inequality is
`\(x \geq a\)`, signifying that the function is defined and graphed for values of \(x\) greater than or equal to \(a\).

In practical terms, if the leftmost point on the graph is at \(x = a\), any \(x\) value to the right of \(a\) is included in the domain. The inequality
`\(x \geq a\)` ensures that all such values are considered, covering the entire part of the exponential function shown on the grid. This concept aligns with the nature of exponential functions, where the domain extends indefinitely to the right on the x-axis.

In conclusion, the inequality
`\(x \geq a\)` accurately captures the domain of the part of the exponential function graphed. This choice is rooted in the fundamental idea that the function is defined for all (x\) values greater than or equal to the leftmost point on the graph.