Question

let \\(f(x) = \frac{84 - 2x^2}{3x^2 - 108}\\).

a) find the \\(y\\)-intercept(s) of \\(f(x)\\). list your answers as points in the form \\((a, b)\\). separate multiple intercepts with commas if necessary.

b) find the \\(x\\)-intercept(s) of \\(f(x)\\). list your answers as points in the form \\((a, b)\\). separate multiple intercepts with commas if necessary.

Explanation:

Evaluate the function at x = 0

$$ f(0) = \frac{84 - 2(0)^2}{3(0)^2 - 108} = \frac{84}{-108} = -\frac{7}{9} $$

Find the roots of the numerator

$$
LATEXBLOCK0
$$

Check the domain of the function

$$
LATEXBLOCK1
$$

Since \(\pm\sqrt{42}
e \pm 6\), both values are in the domain.

Answer:

Question a

\((0, -\frac{7}{9})\)

Question b

\((\sqrt{42}, 0), (-\sqrt{42}, 0)\)