Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 35E
Related questions
Question
The correct equation is f(×)= the correct equation is not y=
![### Find an equation for the graph sketched below
The image illustrates a graph with the following characteristics:
- The x-axis ranges from -5 to 5.
- The y-axis ranges from -8 to 8.
- The graph appears to be an exponential function.
**Detailed Analysis:**
- As x approaches negative values, the function approaches 0 but never quite reaches it.
- As x increases, the value of the function f(x) increases rapidly.
- There's an exponential growth pattern, which commonly suggests a function of the type \( f(x) = a \cdot b^x \).
Based on the graph's behavior, where it appears to rise exponentially, a probable general form for the function might be:
\[ f(x) = e^x \]
This can be written more generally as:
\[ f(x) = a \cdot b^x \]
To confirm the exact equation, one would typically need to verify specific points on the graph and solve for the constants \(a\) and \(b\) accordingly. Given the exponential nature and the general appearance, this fits the description well as an exponential growth function.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6a66d878-2f58-4b17-a7a9-b61e2abefcf5%2Feabbf4da-85df-4ec5-a678-1919d67947dc%2Fvjik37_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Find an equation for the graph sketched below
The image illustrates a graph with the following characteristics:
- The x-axis ranges from -5 to 5.
- The y-axis ranges from -8 to 8.
- The graph appears to be an exponential function.
**Detailed Analysis:**
- As x approaches negative values, the function approaches 0 but never quite reaches it.
- As x increases, the value of the function f(x) increases rapidly.
- There's an exponential growth pattern, which commonly suggests a function of the type \( f(x) = a \cdot b^x \).
Based on the graph's behavior, where it appears to rise exponentially, a probable general form for the function might be:
\[ f(x) = e^x \]
This can be written more generally as:
\[ f(x) = a \cdot b^x \]
To confirm the exact equation, one would typically need to verify specific points on the graph and solve for the constants \(a\) and \(b\) accordingly. Given the exponential nature and the general appearance, this fits the description well as an exponential growth function.
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