Find the Range y = log of x+2

Problem

y=(log_)(x+2)

Solution

1. Identify the type of function. The given function is a logarithmic function of the form y=(log_b)(u) where the base b is typically assumed to be 10 or e

2. Recall the properties of logarithmic functions. For any base b>1 or 0<b<1 the domain is restricted to (x+2)>0 but the output y can take any real value.

3. Analyze the behavior of the function as the argument approaches its limits. As x→−2^+ the value of (log_)(x+2)→−∞ As x→∞ the value of (log_)(x+2)→∞

4. Determine the range based on the continuity of the logarithmic function. Since the function is continuous on its domain and spans from negative infinity to positive infinity, the range is the set of all real numbers.

Final Answer

Range:(−∞,∞)

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