Question
When comparing linear, quadratic, and exponential functions, what key feature do all three function types share?
A) The x-intercept of all four function types is (0,0)
B) The domain of all four function types is all real numbers
C) The range of all four function types is all real numbers
D) The minimum value of all function types is (0,0)
A) The x-intercept of all four function types is (0,0)
B) The domain of all four function types is all real numbers
C) The range of all four function types is all real numbers
D) The minimum value of all function types is (0,0)
Answers
GPT-4o mini
The correct answer is **B) The domain of all four function types is all real numbers**.
All three types of functions—linear, quadratic, and exponential—have a domain that includes all real numbers.
Here's a brief explanation for the other options:
A) The x-intercept of all four function types is not necessarily (0,0). For example, a linear function can have a different x-intercept, and exponential functions are typically greater than zero for all real x values, thus they don’t have an x-intercept at (0,0).
C) The range of these functions differs. Linear functions can have any real value as their range, while quadratic functions range from their vertex value to infinity (or negative infinity depending on the orientation), and exponential functions are typically limited to positive values.
D) Not all function types have a minimum value of (0,0). For example, quadratic functions can have a minimum value that is above zero, and linear functions can also take negative values. Exponential functions do not reach zero, and their minimum value is asymptotic to the x-axis.
Thus, the best choice that applies to all three is B.
All three types of functions—linear, quadratic, and exponential—have a domain that includes all real numbers.
Here's a brief explanation for the other options:
A) The x-intercept of all four function types is not necessarily (0,0). For example, a linear function can have a different x-intercept, and exponential functions are typically greater than zero for all real x values, thus they don’t have an x-intercept at (0,0).
C) The range of these functions differs. Linear functions can have any real value as their range, while quadratic functions range from their vertex value to infinity (or negative infinity depending on the orientation), and exponential functions are typically limited to positive values.
D) Not all function types have a minimum value of (0,0). For example, quadratic functions can have a minimum value that is above zero, and linear functions can also take negative values. Exponential functions do not reach zero, and their minimum value is asymptotic to the x-axis.
Thus, the best choice that applies to all three is B.