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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.

Exp Function

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 .

Exp Function

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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