Describe the end behavior of the function y=logx

Question

𝑦
=
log
⁡
𝑥
.(1 point)
Responses

As x→0+
𝑥
→
0
+
, y→∞
𝑦
→
∞
, and as x→∞
𝑥
→
∞
, y→−∞
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→−∞
𝑥
→
−
∞
, y→−∞
𝑦
→
−
∞
, and as x→∞
𝑥
→
∞
, y→∞
𝑦
→
∞
.
As x right arrow negative infinity , y right arrow negative infinity , and as x right arrow infinity , y right arrow infinity .

As x→−∞
𝑥
→
−
∞
, y→−∞
𝑦
→
−
∞
, and as x→0
𝑥
→
0
, y→∞
𝑦
→
∞
.
As x right arrow negative infinity , y right arrow negative inifinity , and as x right arrow 0 , y right arrow infinity .

As x→0+
𝑥
→
0
+
, y→−∞
𝑦
→
−
∞
, and as x→∞
𝑥
→
∞
, y→∞
𝑦
→
∞
.

Answer 1

To analyze the end behavior of the function \( y = \log x \):

1. As \( x \to 0^+ \): The logarithm function approaches infinity. Mathematically, as \( x \) gets closer to 0 from the positive side, \( y = \log x \) tends to \( +\infty \).

2. As \( x \to \infty \): The logarithm function increases without bound, but at a slower rate than polynomial or exponential functions. Therefore, as \( x \) approaches infinity, \( y = \log x \) tends to \( +\infty \).

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

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

It seems there is no option that precisely matches this exact description. However, we can eliminate the incorrect statements you provided.

The correct response to choose based on the behaviors described will be:

"As \( x \to 0^+ \), \( y \to \infty\), and as \( x \to \infty\), \( y \to \infty \)." (Recheck if an option matches closely to this.)