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C. 723 Quls: Grophing Exporiental Functione
What is the range of $f(x)=-6 \cdot 2^{x}$ ?
A. All real numbers
B. $y< 0$
C. $y< 1$
D. $y> 0$
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Answer
Therefore, the range of the function is all negative real numbers, which can be written in interval notation as \(\boxed{(-\infty, 0)}\).
Step 1 ：First, observe that the function is an exponential function with a negative coefficient, which means it will be decreasing and always negative.
Step 2 ：Since the function is always negative, the range of the function will only include negative numbers.
Step 3 ：As x approaches positive infinity, the function will approach 0 from the negative side, but it will never actually reach 0.
Step 4 ：As x approaches negative infinity, the function will decrease without bound, meaning it can take on any large negative value.
Step 5 ：Therefore, the range of the function is all negative real numbers, which can be written in interval notation as \(\boxed{(-\infty, 0)}\).
