Question

which statement accurately analyzes a key feature of a logarithmic parent function? (1 point)
the logarithmic parent function has a limited domain.
the logarithmic parent function can have multiple x - intercepts.
the logarithmic parent function is an even function.
the logarithmic parent function has only one y - intercept.

Explanation:

• The logarithmic parent function is \(y = \log_{a}(x)\) (\(a>0,a

eq1\)).

• Domain: For \(y = \log_{a}(x)\), the argument \(x>0\). So the domain is \((0,\infty)\), which is a limited domain.
• \(x\) - intercept: Set \(y = 0\), then \(\log_{a}(x)=0\), which gives \(x = 1\) (since \(a^{0}=1\)). So there is only one \(x\) - intercept.
• Even function: A function \(y = f(x)\) is even if \(f(-x)=f(x)\). For \(y=\log_{a}(x)\), \(f(-x)=\log_{a}(-x)\) is not defined for real numbers when \(x>0\) (domain of \(y = \log_{a}(x)\) is \(x>0\)), so it is not an even function.
• \(y\) - intercept: Set \(x = 0\), then \(y=\log_{a}(0)\) is undefined. So there is no \(y\) - intercept.

Answer:

The logarithmic parent function has a limited domain.