Common Mistakes

Frequent Errors

1. Writing Dom as all real numbers. 2. Claiming a horizontal asymptote instead of VA $x=0$. 3. Identifying a turning point or inflection on $(0,\infty)$. 4. Wrong limit direction as $x\to 0^+$ or $x\to\infty$. 5. Assuming every log is increasing. 6. Forgetting Range is all reals. 7. Confusing features of $b^x$ with $\log_b x$. 8. Ignoring that closed intervals can create endpoint extrema.

Why These Happen

Students import exponential end-behavior language and parabola "vertex" ideas onto log graphs.

How to Fix Them

• Feature checklist every time: Dom, Range, VA, mono, concavity, limits.
• Sketch $(1,0)$ and the asymptote first.
• Compare one increasing and one decreasing log side by side.

Avoidance Scripts

• "Dom is greater than zero; never touch $x=0$."
• "Always increasing or always decreasing — no turn."
• "Vertical asymptote at zero; unbounded ends."

Quick Self-Check

• Dom and Range correct?
• VA named?
• Limits stated both ways?
• Extrema/inflection only if closed interval given?