Question

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

Answer 1

The most accurate statement regarding a key feature of the logarithmic parent function is: **The logarithmic parent function has only one y-intercept.**

To elaborate:

1. **X-intercepts**: The logarithmic parent function (y = log(x)) does not have multiple x-intercepts; in fact, it has only one x-intercept at (1, 0).

2. **Y-intercept**: The function has only one y-intercept, which occurs at (1, 0). As x approaches 0 from the right, the function approaches negative infinity, and it does not cross the y-axis for values of x less than or equal to 0.

3. **Even function**: The logarithmic function is not an even function (f(-x) ≠ f(x)), as its graph is not symmetric about the y-axis.

4. **Limited domain**: The logarithmic function does have a limited domain; it only exists for x > 0. However, the statement regarding the y-intercept is more specific and accurate for what the question asks regarding a key feature.

So, the best answer here is that the logarithmic parent function has only one y-intercept.