Science:Math Exam Resources/Courses/MATH110/April 2011/Question 08 (c)/Solution 1

At a function's x-intercept, its y-value is equal to zero. Thus to find our x-intercepts, we need to set the function equal to 0 and solve for $x$.

$0=\ln(4-x^{2})$

We raise both sides by e to cancel the logarithm and get:

${\begin{aligned}e^{0}&=e^{\ln(4-x^{2})}\\1&=4-x^{2}\\x^{2}&=3\\\pm {\sqrt {3}}&=x\end{aligned}}$

So our two x-intercepts are at $x=\pm {\sqrt {3}}$.

The y-intercept of a function occurs when $x=0$. Therefore the y-intercept is $\displaystyle {}y=\ln {4}$.