Describe the end behavior of the function y=logx .(1 point) Responses As x→0+ , y→−∞ , and as x→∞ , y→∞ . As x right arrow 0 superscript positive baseline , y right arrow negative inifinity , and as x right arrow inifinity , y right arrow infinity . As x→−∞ , y→−∞ , and as x→∞ , y→∞ . As x right arrow negative infinity , y right arrow negative infinity , and as x right arrow infinity , y right arrow infinity . As x→0+ , y→∞ , and as x→∞ , y→−∞ . As x right arrow 0 superscript positive baseline , y right arrow infinity , and as x right arrow infinity , y right arrow negative inifinity . As x→−∞ , y→−∞ , and as x→0 , y→∞ .

Question

GPT-4o mini · Answer

To describe the end behavior of the function \( y = \log x \), we need to consider the two limits of the function as \( x \) approaches zero from the right and as \( x \) approaches positive infinity:

As \( x \to 0^+ \) (which means \( x \) approaches 0 from the positive side), the value of \( y = \log x \) approaches negative infinity. That is, \( y \to -\infty \).
As \( x \to \infty \) (as \( x \) increases without bound), the value of \( y = \log x \) approaches positive infinity. That is, \( y \to \infty \).

Thus, the correct description of the end behavior of the function \( y = \log x \) is:

As \( x \to 0^+ \), \( y \to -\infty \), and as \( x \to \infty \), \( y \to \infty \).