Thinking exponential graphs cross the x-axis H
"The Impossible Intercept"
The Mistake in Action
Student draws $y = 2^x$ with an x-intercept at some negative value.
Why It Happens
Students see the curve getting very close to the x-axis and assume it eventually crosses.
The Fix
For $y = a^x$ where $a > 0$:
- $a^x$ is always positive (no matter what x is)
- The x-axis is an asymptote – the curve approaches but never reaches it
- When $x$ is very negative, $a^x$ is very small but still positive
Example: $2^{-10} = \frac{1}{1024} \approx 0.001$ (small but positive!)
The only way to get y = 0 would be if $2^x = 0$, which is impossible.
Spot the Mistake
Can you identify where this student went wrong?
$y = 2^x$
crosses the x-axis at negative x
Click on the line that contains the error.
Related Topics
Learn more about the underlying maths: