Question
Question
Compare the linear, exponential, and quadratic functions shown. Determine whether each statement is true or false.
number 1 main points are (0,-3) (6,0)
number 2 main points are (0,2)(-5,0)
number 3 main points are (-2.5,0) (0,-2.5)(2.5,0)
(3 points)
True False
All 3 functions have a domain of all real numbers.
The quadratic function has a range of a real numbers.
The linear function has a range of all real numbers.
Compare the linear, exponential, and quadratic functions shown. Determine whether each statement is true or false.
number 1 main points are (0,-3) (6,0)
number 2 main points are (0,2)(-5,0)
number 3 main points are (-2.5,0) (0,-2.5)(2.5,0)
(3 points)
True False
All 3 functions have a domain of all real numbers.
The quadratic function has a range of a real numbers.
The linear function has a range of all real numbers.
Answers
GPT-4o mini
Let's analyze each statement based on the provided points for the three functions:
1. **All 3 functions have a domain of all real numbers.**
- **True**: Linear, exponential, and quadratic functions are defined for all real numbers. Therefore, this statement is true.
2. **The quadratic function has a range of all real numbers.**
- **False**: The range of a quadratic function depends on its vertex and direction (concave up or concave down). Typically, quadratic functions do not cover all real numbers; they either have a maximum or minimum value and thus have a restricted range. For example, if a quadratic opens upwards, the range will start from the minimum value to positive infinity, and if it opens downwards, the range will start from negative infinity up to the maximum value.
3. **The linear function has a range of all real numbers.**
- **True**: Linear functions can take any value along the y-axis as their x-values change. Since the linear function has no restrictions on its output, this statement is true.
**Summary of answers:**
1. True
2. False
3. True
1. **All 3 functions have a domain of all real numbers.**
- **True**: Linear, exponential, and quadratic functions are defined for all real numbers. Therefore, this statement is true.
2. **The quadratic function has a range of all real numbers.**
- **False**: The range of a quadratic function depends on its vertex and direction (concave up or concave down). Typically, quadratic functions do not cover all real numbers; they either have a maximum or minimum value and thus have a restricted range. For example, if a quadratic opens upwards, the range will start from the minimum value to positive infinity, and if it opens downwards, the range will start from negative infinity up to the maximum value.
3. **The linear function has a range of all real numbers.**
- **True**: Linear functions can take any value along the y-axis as their x-values change. Since the linear function has no restrictions on its output, this statement is true.
**Summary of answers:**
1. True
2. False
3. True