QuestionWhat is the end behavior of the reflected cubic function as approaches negative infinity? Choose: a. , b. , c. , d. $f(x) \to 3.
Studdy Solution
STEP 1
Assumptions1. The original function is a cubic parent function, which is typically represented as .
. The function is reflected across the -axis, which means the new function is .
3. We are interested in the end behavior of the function as approaches negative infinity.
STEP 2
The end behavior of a function describes the trend of the function values as approaches positive infinity or negative infinity.
STEP 3
For the original cubic parent function , as approaches negative infinity, also approaches negative infinity. This is because the cube of a large negative number is also a large negative number.
STEP 4
However, the function has been reflected across the -axis. This means that wherever the original function had a positive -value, the reflected function has a negative -value, and vice versa.
STEP 5
So, for the reflected function , as approaches negative infinity, approaches positive infinity. This is because the negative of a large negative number is a large positive number.
Therefore, the correct answer is (b) approaches positive infinity.
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