Question
Compare the linear, quadratic, and exponential functions shown.
(2 points)
All three functions have a
of all real numbers, but only the linear function has a
of all real numbers.
(2 points)
All three functions have a
of all real numbers, but only the linear function has a
of all real numbers.
Answers
Answered by
GPT-4o mini
To compare the linear, quadratic, and exponential functions, we can consider their domains and ranges.
1. **Domain**: All three functions (linear, quadratic, and exponential) have a **domain** of all real numbers. This means you can input any real number into all of these functions.
2. **Range**:
- The **linear function** has a **range** of all real numbers because it can take any value as output, depending on the slope and y-intercept.
- The **quadratic function** typically has a **range** of all real numbers greater than or equal to (or less than or equal to) a specific value, depending on whether the parabola opens upward or downward. This means its range is limited compared to the linear function.
- The **exponential function** has a **range** that is usually positive real numbers (or real numbers greater than zero). This means it does not take on any negative values or zero, unlike the linear function.
So, the completed statement is:
"All three functions have a **domain** of all real numbers, but only the linear function has a **range** of all real numbers."
1. **Domain**: All three functions (linear, quadratic, and exponential) have a **domain** of all real numbers. This means you can input any real number into all of these functions.
2. **Range**:
- The **linear function** has a **range** of all real numbers because it can take any value as output, depending on the slope and y-intercept.
- The **quadratic function** typically has a **range** of all real numbers greater than or equal to (or less than or equal to) a specific value, depending on whether the parabola opens upward or downward. This means its range is limited compared to the linear function.
- The **exponential function** has a **range** that is usually positive real numbers (or real numbers greater than zero). This means it does not take on any negative values or zero, unlike the linear function.
So, the completed statement is:
"All three functions have a **domain** of all real numbers, but only the linear function has a **range** of all real numbers."