Question
Match the following characteristics with there parent function(s)
Functions:
Linear
Absolute value
Quadratic
Square Root
Cubic
Cube Root
Rational
Exponentional
Logarithmic
None
Characteristics:
Its graph passes through the origin
Its graph does not touch the x-axis
For all values of x in its domain y increases as x increases
Its graph never touches Quadrant II or IV
Bothe its domain and range consist of all real numbers
Its graph never touches the y-axis
Its graph is symmetric about the y-axis its range values are all non-negative
For all values of x, y values increase at a constant rate
Its graph is symmetric about the x-axis
Its domain values are all non-negative
Its graph is not countinuous
Its domain values and range values are non-negative
Its range values are negative when domain values are negative
Its domain and range values consist of all real numbers except zero
Functions:
Linear
Absolute value
Quadratic
Square Root
Cubic
Cube Root
Rational
Exponentional
Logarithmic
None
Characteristics:
Its graph passes through the origin
Its graph does not touch the x-axis
For all values of x in its domain y increases as x increases
Its graph never touches Quadrant II or IV
Bothe its domain and range consist of all real numbers
Its graph never touches the y-axis
Its graph is symmetric about the y-axis its range values are all non-negative
For all values of x, y values increase at a constant rate
Its graph is symmetric about the x-axis
Its domain values are all non-negative
Its graph is not countinuous
Its domain values and range values are non-negative
Its range values are negative when domain values are negative
Its domain and range values consist of all real numbers except zero
Answers
Answered by
GPT-4o mini
Let's match the characteristics with their parent functions:
1. **Its graph passes through the origin**
- **Linear** (e.g., y = mx + b, where b = 0)
2. **Its graph does not touch the x-axis**
- **Exponential** (e.g., y = e^x or any positive base), as the function never crosses the x-axis.
3. **For all values of x in its domain y increases as x increases**
- **Exponential** (for positive bases) or **Linear** (if you consider only positive slopes)
4. **Its graph never touches Quadrant II or IV**
- **Exponential** (e.g., y = e^x), as it never has negative y-values.
5. **Both its domain and range consist of all real numbers**
- **Cubic** (e.g., y = x^3) or **Linear** (e.g., y = mx + b)
6. **Its graph never touches the y-axis**
- **Rational** (e.g., y = 1/x), as it has a vertical asymptote at x = 0.
7. **Its graph is symmetric about the y-axis its range values are all non-negative**
- **Absolute value** (e.g., y = |x|).
8. **For all values of x, y values increase at a constant rate**
- **Linear** (e.g., y = mx + b) with a positive slope.
9. **Its graph is symmetric about the x-axis**
- **Odd function** (e.g., y = x^3, which is not symmetric about the x-axis but reflects through it).
10. **Its domain values are all non-negative**
- **Square Root** (e.g., y = √x).
11. **Its graph is not continuous**
- **Rational** (e.g., y = 1/x), which has a discontinuity at x = 0.
12. **Its domain values and range values are non-negative**
- **Absolute value** (e.g., y = |x|) or **Square Root** (e.g., y = √x).
13. **Its range values are negative when domain values are negative**
- **Quadratic** (e.g., y = -x^2), which opens downwards and has negative range when x is negative.
14. **Its domain and range values consist of all real numbers except zero**
- **Rational** (e.g., y = 1/x), which cannot accept x = 0.
To summarize:
- Linear: 1, 3, 5, 8
- Absolute Value: 7, 12
- Quadratic: 13
- Square Root: 10
- Cubic: 5
- Cube Root: None
- Rational: 6, 11, 14
- Exponential: 2, 3, 4
- Logarithmic: None
- None: 9 (as a specific symmetrical function doesn't apply to listed families).
1. **Its graph passes through the origin**
- **Linear** (e.g., y = mx + b, where b = 0)
2. **Its graph does not touch the x-axis**
- **Exponential** (e.g., y = e^x or any positive base), as the function never crosses the x-axis.
3. **For all values of x in its domain y increases as x increases**
- **Exponential** (for positive bases) or **Linear** (if you consider only positive slopes)
4. **Its graph never touches Quadrant II or IV**
- **Exponential** (e.g., y = e^x), as it never has negative y-values.
5. **Both its domain and range consist of all real numbers**
- **Cubic** (e.g., y = x^3) or **Linear** (e.g., y = mx + b)
6. **Its graph never touches the y-axis**
- **Rational** (e.g., y = 1/x), as it has a vertical asymptote at x = 0.
7. **Its graph is symmetric about the y-axis its range values are all non-negative**
- **Absolute value** (e.g., y = |x|).
8. **For all values of x, y values increase at a constant rate**
- **Linear** (e.g., y = mx + b) with a positive slope.
9. **Its graph is symmetric about the x-axis**
- **Odd function** (e.g., y = x^3, which is not symmetric about the x-axis but reflects through it).
10. **Its domain values are all non-negative**
- **Square Root** (e.g., y = √x).
11. **Its graph is not continuous**
- **Rational** (e.g., y = 1/x), which has a discontinuity at x = 0.
12. **Its domain values and range values are non-negative**
- **Absolute value** (e.g., y = |x|) or **Square Root** (e.g., y = √x).
13. **Its range values are negative when domain values are negative**
- **Quadratic** (e.g., y = -x^2), which opens downwards and has negative range when x is negative.
14. **Its domain and range values consist of all real numbers except zero**
- **Rational** (e.g., y = 1/x), which cannot accept x = 0.
To summarize:
- Linear: 1, 3, 5, 8
- Absolute Value: 7, 12
- Quadratic: 13
- Square Root: 10
- Cubic: 5
- Cube Root: None
- Rational: 6, 11, 14
- Exponential: 2, 3, 4
- Logarithmic: None
- None: 9 (as a specific symmetrical function doesn't apply to listed families).
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