Questions: Examine the following function: h(x) = log base 1 of x Which graph represents the function?

Transcript text: Examine the following function: \[ h(x)=\log _{1} x \] Which graph represents the function?

Solution

Solution Steps

Step 1: Analyze the given function

The given function is \(h(x) = \log_1 x\). Logarithms with a base of 1 are undefined. This is because the logarithmic function \(y = \log_b x\) is the inverse of the exponential function \(b^y = x\). If \(b=1\), the exponential function becomes \(1^y = x\), which means \(x=1\) for all values of \(y\). This is a vertical line and not a function, so it doesn't have an inverse. Therefore, \(h(x) = \log_1 x\) is not a valid logarithmic function.

Step 2: Relate to the Graph

Since the base-1 logarithm is undefined, it cannot be represented by any graph. The graph shown in the image resembles a logarithmic function with a base greater than 1, but it's crucial to understand that the provided function itself is invalid.

Step 3: Conclusion

The provided graph cannot represent \(h(x) = \log_1 x\) because the function itself is undefined. No graph can represent a base-1 logarithm.