Write the domain of $ f $ in interval notation. Enter $ -\infty $ as -INF, $ \infty $ as INF, and $ \cup $ (union) as U.**Domain of $ f $:**[Input Box][Submit Answer] Tries 0/99---Write the range of $ f $ in interval notation. Enter $ -\infty $ as -INF, $ \infty $ as INF, and $ \cup $ (union) as U.**Range of $ f $:**[Input Box][Submit Answer] Tries 0/99---Find $ f(-1) $. If the function is undefined for the input $-1$, type **UNDEFINED**.$ f(-1) = $[Input Box][Submit Answer] Tries 0/99 The image displays a graph of the natural logarithm function, $ y = \ln(x) $.**Graph Description:**- **Axes and Scale:** - The horizontal axis (x-axis) ranges from -1 to 9. - The vertical axis (y-axis) ranges from -4 to 4. - Both axes are labeled with increments of 1.- **Curve Characteristics:** - The curve is drawn in red. - It starts from a point approaching negative infinity as it gets closer to the y-axis from the right, reflecting the property that the logarithm of 0 is undefined. - The curve passes through the point (1, 0), illustrating that $\ln(1) = 0$. - It increasingly grows at a decelerating rate as x-values increase, indicating a logarithmic growth pattern.**Behavior of the Logarithmic Function:**- The graph is only defined for positive values of $x$.- For $x > 0$: The function indicates a slow, continuous increase in y-values as x increases.- As $x$ approaches 0 from the right, the value of $y = \ln(x)$ tends toward negative infinity.This graph is commonly used to demonstrate how logarithmic functions behave, especially their growth dynamics and intercepts.

Write the domain of f in interval notation. Enter -0 as -INF, Co as INF, and U (union) as U. Domain of f : Submit Answer Tries 0/99 Write the range of f in interval notation. Enter -0 as -INF, o as INF, and U (union) as U. Range of f : Submit Answer Tries 0/99 Find f (-1) . If the function is undefined for the input -1, type UNDEFINED . f(-1) =

Write the domain of f in interval notation. Enter -0 as -INF, Co as INF, and U (union) as U. Domain of f : Submit Answer Tries 0/99 Write the range of f in interval notation. Enter -0 as -INF, o as INF, and U (union) as U. Range of f : Submit Answer Tries 0/99 Find f (-1) . If the function is undefined for the input -1, type UNDEFINED . f(-1) =

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

Write the domain of $ f $ in interval notation. Enter $ -\infty $ as -INF, $ \infty $ as INF, and $ \cup $ (union) as U.

**Domain of $ f $:**
[Input Box]

[Submit Answer] Tries 0/99

---

Write the range of $ f $ in interval notation. Enter $ -\infty $ as -INF, $ \infty $ as INF, and $ \cup $ (union) as U.

**Range of $ f $:**
[Input Box]

[Submit Answer] Tries 0/99

---

Find $ f(-1) $. If the function is undefined for the input $-1$, type **UNDEFINED**.

$ f(-1) = $
[Input Box]

[Submit Answer] Tries 0/99

The image displays a graph of the natural logarithm function, $ y = \ln(x) $.

**Graph Description:**

- **Axes and Scale:**
- The horizontal axis (x-axis) ranges from -1 to 9.
- The vertical axis (y-axis) ranges from -4 to 4.
- Both axes are labeled with increments of 1.

- **Curve Characteristics:**
- The curve is drawn in red.
- It starts from a point approaching negative infinity as it gets closer to the y-axis from the right, reflecting the property that the logarithm of 0 is undefined.
- The curve passes through the point (1, 0), illustrating that $\ln(1) = 0$.
- It increasingly grows at a decelerating rate as x-values increase, indicating a logarithmic growth pattern.

**Behavior of the Logarithmic Function:**

- The graph is only defined for positive values of $x$.
- For $x > 0$: The function indicates a slow, continuous increase in y-values as x increases.
- As $x$ approaches 0 from the right, the value of $y = \ln(x)$ tends toward negative infinity.

This graph is commonly used to demonstrate how logarithmic functions behave, especially their growth dynamics and intercepts.

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