Question

Which of the following curve has no asymptote:

• A. $y=5^x$
• B. $y={\log }_{e}x$
• C. $y=x^2-3x+2$
• D. $x^2-4y^2=4$

Answer 1

The correct option is C $y=x^2-3x+2$

For $y=5^x,$ As $x\to -\infty$ gives $y=0$ is a horizontal asymptote.
For $y={\log }_{e}x,$ As $x\to 0^{+}$ gives $y\to -\infty .$ So, $x=0$ is a vertical asymptote.
For $y=x^2-3x+2,$ is a parabola
So, no any asymptotes.
For $x^2-4y^2=4,$ is hperbola.
So, two asymptotes.