Question

If we draw the graph of \(f(x) = \log_{10(x + 1)\) on the domain of definition, which quadrants does it pass through?}

• A. First and third
• B. First and fourth
• C. First and second
• D. Second and fourth

Hint:

Remember: \(\log(u)\) is positive when \(u>1\) and negative when \(0<u<1\). Check the sign of x and y in these regions.

Answer 1

The Correct Option is A

Step 1: Domain Analysis:
\(x + 1>0 \implies x>-1\).
The graph exists for \(x>-1\).
Step 2: Quadrant Analysis:
1. If \(x>0\), then \(x+1>1\). \(\log_{10}(x+1)>0\). (Positive x, Positive y) \(\to\) 1st Quadrant.
2. If \(-1<x<0\), then \(0<x+1<1\). \(\log_{10}(x+1)<0\).
(Negative x, Negative y) \(\to\) 3rd Quadrant. The graph passes through Q1 and Q3.