Which types of parent function have the end behavior f(x) -> -infinity as x-> -infinity? Select all that apply.
a parent even-degree power function
a parent odd-degree power function
a parent even-degree root function
a parent odd-degree root function
a parent exponential function with a base greater than 1
a parent exponential function with a base between 0 and 1
a parent logarithmic function with a base greater than 1
a parent logarithmic function with a base between 0 and 1
The parent functions that have the end behavior f(x) -> -infinity as x -> -infinity are:
- A parent odd-degree power function
- A parent exponential function with a base between 0 and 1
The types of parent function that have the end behavior f(x) -> -infinity as x -> -infinity are:
- A parent odd-degree power function
- A parent exponential function with a base between 0 and 1
So, the correct options are:
- A parent odd-degree power function
- A parent exponential function with a base between 0 and 1
To determine the end behavior of a function, we analyze what happens to the function as x approaches positive or negative infinity.
1. A parent even-degree power function:
- As x approaches negative infinity, the function goes to positive infinity.
- As x approaches positive infinity, the function goes to positive infinity.
Since the function does not approach negative infinity as x approaches negative infinity, it is not a correct choice.
2. A parent odd-degree power function:
- As x approaches negative infinity, the function goes to negative infinity.
- As x approaches positive infinity, the function goes to positive infinity.
This is a valid choice since the function approaches negative infinity as x approaches negative infinity.
3. A parent even-degree root function:
- As x approaches negative infinity, the function goes to positive infinity.
- As x approaches positive infinity, the function goes to positive infinity.
Since the function does not approach negative infinity as x approaches negative infinity, it is not a correct choice.
4. A parent odd-degree root function:
- As x approaches negative infinity, the function goes to negative infinity.
- As x approaches positive infinity, the function goes to positive infinity.
This is a valid choice since the function approaches negative infinity as x approaches negative infinity.
5. A parent exponential function with a base greater than 1:
- As x approaches negative infinity, the function goes to 0 (approaches positive infinity only if the exponent is negative).
- As x approaches positive infinity, the function goes to positive infinity.
Since the function does not approach negative infinity as x approaches negative infinity, it is not a correct choice.
6. A parent exponential function with a base between 0 and 1:
- As x approaches negative infinity, the function goes to positive infinity.
- As x approaches positive infinity, the function goes to 0 (approaches positive infinity only if the exponent is negative).
Since the function does not approach negative infinity as x approaches negative infinity, it is not a correct choice.
7. A parent logarithmic function with a base greater than 1:
- As x approaches negative infinity, the function is undefined.
- As x approaches positive infinity, the function goes to positive infinity.
Since the function is undefined as x approaches negative infinity, it is not a correct choice.
8. A parent logarithmic function with a base between 0 and 1:
- As x approaches negative infinity, the function is undefined.
- As x approaches positive infinity, the function goes to negative infinity.
Since the function is undefined as x approaches negative infinity, it is not a correct choice.
Based on the analysis, the types of parent function that have the end behavior f(x) -> -infinity as x -> -infinity are:
- A parent odd-degree power function
- A parent odd-degree root function
Therefore, the correct choices are:
- A parent odd-degree power function
- A parent odd-degree root function