Lynn Ellis has taught mathematics to high gear school and residential district college students for over 13 years. She has a Bachelor ‘s degree in Mathematics from Middlebury College and a Master ‘s Degree in education from the University of Phoenix. Jiwon has a B.S. degree in the mathematics/ science field and over 4 years of tutoring have. She fell in beloved with mathematics when she discovered geometry proofread and that tartar can help her identify the world around her like never earlier .

Table of Contents

## Finding the Asymptote Given a Graph of an Exponential Function

**Step 1:** Examine how the graph behaves as { equivalent } x { /eq } increases and as { equivalent } x { /eq } decreases. An exponential function has a horizontal asymptote. When the graph of an exponential affair is near the horizontal asymptote, the graph looks like it is **slowing down** and starts to flatten out, although it never actually becomes categoric .

**Step 2:** Identify the horizontal agate line the graph is approaching. A general equality for a horizontal argumentation is : { eq } y = c { /eq } .

## How to Find the Asymptote Given a Graph of an Exponential Function Vocabulary

**Asymptote** : An asymptote is a production line that the arch of a graph approaches, but never reaches. An asymptote can be a vertical line or a horizontal note .

Let ‘s use these steps, formulas, and definitions to work through two examples of finding the asymptote given a graph of an exponential affair .

## How to Find the Asymptote Given a Graph of an Exponential Function: Example 1

Given the graph of an exponential function below, determine the equation of the horizontal asymptote.

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**Step 1:** Examine how the graph behaves as { equivalent } x { /eq } increases and as { equivalent } x { /eq } decreases. To find a horizontal asymptote in the given graph of an exponential officiate, identify the separate of the graph that looks like it is flattening out. In the time interval { equivalent } [ -4,0 ] { /eq }, the graph looks like it starts to slow down. then, near { equivalent } x = -4 { /eq }, the graph starts to flatten .

We are identical close to finding the horizontal asymptote .

**Step 2:** Identify the horizontal lineage the graph is approaching. Looking closely at the share of the graph you identified in gradation 1, we see that the graph moves slowly down to a course as it moves to the leave on the { equivalent } x { /eq } axis. The agate line that the graph is identical slowly moving toward is the asymptote. **In this graph, the asymptote is {eq}y=2**

**{/eq} .**

## How to Find the Asymptote Given a Graph of an Exponential Function: Example 2

Given the graph of an exponential serve below, determine the equation of the horizontal asymptote .

**Step 1:** Examine how the graph behaves as { equivalent } x { /eq } increases and as { equivalent } x { /eq } decreases. To find a horizontal asymptote in the given graph of an exponential function, identify the part of the graph that looks like it is flattening out .

On the second quadrant of the coordinate plane, the graph quickly decreases, but starts to slow down cheeseparing { equivalent } x = -2 { /eq }. then, we see that the graph importantly slows down in the interval [ 0,3 ]. The graph starts to flatten out near { equivalent } x=3 { /eq }.

**Step 2:** Identify the horizontal line the graph is approaching. Looking closely at the contribution of the graph you identified, { equivalent } x > 3 { /eq }, we see that the graph very slowly moves toward a trace. This line that the graph is approaching is the asymptote, and in this graph, the asymptote is { equivalent } y=-4 { /eq } .

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