Write an equation for the function graphed below 15+ 14+ 13+ 12+ + + + -7 -6 -5 -4 -3 -2 -1 -1 -2 -3 1 2 3 4 5 6 7
Write an equation for the function graphed below 15+ 14+ 13+ 12+ + + + -7 -6 -5 -4 -3 -2 -1 -1 -2 -3 1 2 3 4 5 6 7
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Title: Writing Equations for Graphed Functions**
Welcome to our educational tutorial on writing equations for graphed functions!
Below is the image of a graph showing a function. We'll explore and analyze it to write the corresponding equation.
**Graph Description:**
- The x-axis ranges from -7 to 7.
- The y-axis ranges from -5 to 5.
- There are two vertical asymptotes shown as dashed red lines at \(x = -1\) and \(x = 2\).
**Behavior:**
- For \(x < -1\), the function increases towards positive infinity as it approaches \(x = -1\) and decreases towards negative infinity as \(x\) moves left.
- Between \(x = -1\) and \(x = 2\), the function increases from negative infinity as it approaches \(x = -1\), passes through the y-axis, and continues to increase towards infinity as it approaches \(x = 2\).
- For \(x > 2\), the function starts again from positive infinity and decreases towards zero as \(x\) increases.
**Characteristics:**
- The presence of vertical asymptotes at \(x = -1\) and \(x = 2\) suggests that the function may have factors in the denominator that go to zero at these points.
- The curve's behavior suggests a rational function.
Let's consider the likely equation for this function based on these observations:
\[ y = \frac{A}{(x + 1)(x - 2)} \]
Where \(A\) is a constant that we could solve for using specific points on the graph if necessary.
**Interactive Learning:**
Use the input box below to enter your equation for the graphed function and check if it fits the behavior and asymptotes shown in the graph.
\[ y = \_\_\_\_ \]
Feel free to experiment with different values of \(A\) to see how it affects the graph. Happy learning!](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F70246055-557a-4851-8c33-1313c5079b88%2Fb56b586f-1f02-4782-848c-f5294d87fec1%2Fsq056h8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Writing Equations for Graphed Functions**
Welcome to our educational tutorial on writing equations for graphed functions!
Below is the image of a graph showing a function. We'll explore and analyze it to write the corresponding equation.
**Graph Description:**
- The x-axis ranges from -7 to 7.
- The y-axis ranges from -5 to 5.
- There are two vertical asymptotes shown as dashed red lines at \(x = -1\) and \(x = 2\).
**Behavior:**
- For \(x < -1\), the function increases towards positive infinity as it approaches \(x = -1\) and decreases towards negative infinity as \(x\) moves left.
- Between \(x = -1\) and \(x = 2\), the function increases from negative infinity as it approaches \(x = -1\), passes through the y-axis, and continues to increase towards infinity as it approaches \(x = 2\).
- For \(x > 2\), the function starts again from positive infinity and decreases towards zero as \(x\) increases.
**Characteristics:**
- The presence of vertical asymptotes at \(x = -1\) and \(x = 2\) suggests that the function may have factors in the denominator that go to zero at these points.
- The curve's behavior suggests a rational function.
Let's consider the likely equation for this function based on these observations:
\[ y = \frac{A}{(x + 1)(x - 2)} \]
Where \(A\) is a constant that we could solve for using specific points on the graph if necessary.
**Interactive Learning:**
Use the input box below to enter your equation for the graphed function and check if it fits the behavior and asymptotes shown in the graph.
\[ y = \_\_\_\_ \]
Feel free to experiment with different values of \(A\) to see how it affects the graph. Happy learning!
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