Given the function $f(x) = \frac{x}{x^2 - 400}$
A) What is the polynomial in the denominator of the function?
$x^2 - 400$
$x$
$x^2$
$x - 20$
B) How can we find the value(s) of $x$ that make the denominator zero?
Set the fraction equal to 0 and then solve for $x$
Set the denominator equal to 0 and then solve for $x$
Plug 0 in for $x$ in the numerator and evaluate
Set the numerator equal to 0 and then solve for $x$
Plug 0 in for $x$ in the fraction and evaluate
Plug 0 in for $x$ in the denominator and evaluate
C) What are the $x$-value(s) that make the denominator zero? $x$
D) Therefore, the domain of $f$ consists of all real numbers except:
E) Hence the domain can be expressed in
i. Set notation as {$x$ | $x \neq$ $x \neq$ } or
ii. Interval notation as ($-\infty$, )U( , $\infty$) Draw a real number line and mark the domain if you are unsure of how the interval
would look like.
