Fill in the blank with the correct word from the choices below. 10 -8 -6 -5 -10 -15 20 -35 -40 The function is on the interval (-oo, -2). There is a at -32. There is a at 2. The function is on the interval 2 <<+oo. * positive : negative : zero # y-intercept
Fill in the blank with the correct word from the choices below. 10 -8 -6 -5 -10 -15 20 -35 -40 The function is on the interval (-oo, -2). There is a at -32. There is a at 2. The function is on the interval 2 <<+oo. * positive : negative : zero # y-intercept
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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Question
Fill in the blank with the correct word from the choices below.

Transcribed Image Text:**Educational Resource: Understanding Graphs**
**Graph Analysis**
This graph depicts a function with a complex structure showcasing various behaviors over different intervals.
1. **Graph Details:**
- The graph is plotted on the Cartesian plane with the x-axis labeled from -10 to +8 and the y-axis from -40 to +15.
- The curve intersects the y-axis and shows several peaks and troughs, indicating changes in the function's behavior.
2. **Behavior of the Function:**
- The function is negative on the interval \((-\infty, -2)\). This means that for values of x less than -2, the function lies below the x-axis.
- There is a y-intercept at -32, where the function crosses the y-axis at the point (0, -32).
- There is a zero (root) at -4 and another zero at 2, indicating the x-values where the function crosses the x-axis.
- The function is positive on the interval \(2 < x < +\infty\), meaning that for values of x greater than 2, the function is above the x-axis.
**Fill in the Blanks:**
Choose from: *positive, negative, zero, y-intercept*
- The function is ___negative___ on the interval \((-\infty, -2)\). There is a ___y-intercept___ at -32. There is a ___zero___ at -4 and at 2. The function is ___positive___ on the interval \(2 < x < +\infty\).
Understanding these components is essential for analyzing graphs and identifying function behaviors across different intervals.
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