The graph of f(x) is shown below. Which of the following statements are true? y -7 -6 -3 -2 Select the correct answer below: O f(x) has a removable discontinuity at x = 0. O f(x) has a jump discontinuity at x = 0. O f(x) has an infinite discontinuity at x = 0. Of(x) is continuous at x = 0. -1 00 7 6 5 4 ON 1 0 -1 -2 on -6 -7 1 19 5 6 + 7
The graph of f(x) is shown below. Which of the following statements are true? y -7 -6 -3 -2 Select the correct answer below: O f(x) has a removable discontinuity at x = 0. O f(x) has a jump discontinuity at x = 0. O f(x) has an infinite discontinuity at x = 0. Of(x) is continuous at x = 0. -1 00 7 6 5 4 ON 1 0 -1 -2 on -6 -7 1 19 5 6 + 7
Chapter2: Functions And Their Graphs
Section2.4: A Library Of Parent Functions
Problem 47E: During a nine-hour snowstorm, it snows at a rate of 1 inch per hour for the first 2 hours, at a rate...
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#### Graph Description:
- The graph presents a function \( f(x) \) plotted on a Cartesian plane.
- The x-axis ranges from -8 to 8, and the y-axis ranges from -8 to 8.
- The function exhibits various characteristics, such as peaks, troughs, and points of discontinuity.
- At \( x = 0 \), there is a special point of interest where the function seems to have a discontinuity.
- This point on the graph is marked with an open circle at \( (0, 2) \), indicating the function's value at \( x = 0 \) does not exist there.
- A red dashed vertical line is drawn at \( x = 4 \), highlighting another area of interest in the function.
#### Options for Identifying Discontinuity:
Select the correct answer below:
- \( \circ \) \( f(x) \) has a **removable discontinuity** at \( x = 0 \).
- \( \circ \) \( f(x) \) has a **jump discontinuity** at \( x = 0 \).
- \( \circ \) \( f(x) \) has an **infinite discontinuity** at \( x = 0 \).
- \( \circ \) \( f(x) \) is **continuous** at \( x = 0 \).
#### Explanation of Graphical Features and Terms:
1. **Removable Discontinuity**: Occurs when the function has a hole at \( x = c \), but the limit as \( x \) approaches \( c \) exists.
2. **Jump Discontinuity**: Occurs when the left-hand limit and the right-hand limit as \( x \) approaches \( c \) exist but are not equal.
3. **Infinite Discontinuity**: Occurs when the function approaches infinity (either positive or negative) as \( x \) approaches \( c \).
4. **Continuity**: The function is continuous at \( x = c \) if it is defined at \( c \) and there is no discontinuity at that point.
In this context, choosing the correct type of discontinuity at \( x = 0 \) helps in understanding the nature](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fffcf92b5-4154-452a-af6b-b4e696e552b0%2F5b47f08e-c8f6-4ae6-ba3b-38964f517b23%2Fmpudj06_processed.png&w=3840&q=75)
Transcribed Image Text:### Understanding Discontinuities in Functions
#### The graph of \( f(x) \) is shown below. Which of the following statements are true?
#### Graph Description:
- The graph presents a function \( f(x) \) plotted on a Cartesian plane.
- The x-axis ranges from -8 to 8, and the y-axis ranges from -8 to 8.
- The function exhibits various characteristics, such as peaks, troughs, and points of discontinuity.
- At \( x = 0 \), there is a special point of interest where the function seems to have a discontinuity.
- This point on the graph is marked with an open circle at \( (0, 2) \), indicating the function's value at \( x = 0 \) does not exist there.
- A red dashed vertical line is drawn at \( x = 4 \), highlighting another area of interest in the function.
#### Options for Identifying Discontinuity:
Select the correct answer below:
- \( \circ \) \( f(x) \) has a **removable discontinuity** at \( x = 0 \).
- \( \circ \) \( f(x) \) has a **jump discontinuity** at \( x = 0 \).
- \( \circ \) \( f(x) \) has an **infinite discontinuity** at \( x = 0 \).
- \( \circ \) \( f(x) \) is **continuous** at \( x = 0 \).
#### Explanation of Graphical Features and Terms:
1. **Removable Discontinuity**: Occurs when the function has a hole at \( x = c \), but the limit as \( x \) approaches \( c \) exists.
2. **Jump Discontinuity**: Occurs when the left-hand limit and the right-hand limit as \( x \) approaches \( c \) exist but are not equal.
3. **Infinite Discontinuity**: Occurs when the function approaches infinity (either positive or negative) as \( x \) approaches \( c \).
4. **Continuity**: The function is continuous at \( x = c \) if it is defined at \( c \) and there is no discontinuity at that point.
In this context, choosing the correct type of discontinuity at \( x = 0 \) helps in understanding the nature
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