Problem

ApexLeaming Courses 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. $y>0$ PREVIOUS

Solution

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 \(\boxed{(-\infty, 0)}\).

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