Questions: Find the domain and range of y=log2(8-2x). The domain is: The range is:

Transcript text: Find the domain and range of $y=\log _{2}(8-2 x)$. The domain is: $\square$ The range is : $\square$

Solution

Solution Steps

Step 1: Find the Domain

To find the domain of the function $ y = \log_{2}(8 - 2x) $, we need to solve the inequality $ 8 - 2x > 0 $. This simplifies to $ 2x < 8 $ or $ x < 4 $. Therefore, the domain is all values of $ x $ less than 4, which can be expressed in interval notation as $ (-\infty, 4) $.

Step 2: Find the Range

The range of the function $ y = \log_{2}(8 - 2x) $ is determined by the properties of the logarithmic function. Since the logarithm can take any real number as its output, the range is all real numbers, denoted as $ \mathbb{R} $.