Question

Find the intercepts of the function.g(n) = −3(3n − 1)(4n + 1)n-intercept (n, g(n)) = (smaller n-value)n-intercept (n, g(n)) = (larger n-value)y-intercept (n, g(n)) =

Answer 1

In order to find the n-intercepts of the function, let's equate each factor to zero:

$\begin{gathered} -3(3n-1)(4n+1)=0\\ \\ \begin{cases}3n-1=0\rightarrow n=\frac{1}{3}{} \\ 4n+1=0\rightarrow n=-\frac{1}{4}{}\end{cases} \end{gathered}$

So the n-intercept with the smaller n-value is (-1/4, 0) and the n-intercept with the larger n-value is (1/3, 0).

Now, to find the y-intercept, let's use n = 0 and calculate the value of g(n):

$\begin{gathered} g(n)=-3(3n-1)(4n+1)\\ \\ g(0)=-3(3\cdot0-1)(4\cdot0+1)\\ \\ g(0)=-3(-1)(1)\\ \\ g(0)=3 \end{gathered}$

Therefore the y-intercept is (0, 3).