Questions: Find the intercepts of the function. g(n)=-9(5n-1)(4n+1) n-intercept (n, g(n))=( ) (smaller n-value) n-intercept (n, g(n))=( ) (larger n-value) y-intercept (n, g(n))=( )

Solution Steps

To find the intercepts of the function \( g(n) = -9(5n-1)(4n+1) \), we need to determine where the function intersects the axes.

1. n-intercepts: These occur where \( g(n) = 0 \). Set the equation \(-9(5n-1)(4n+1) = 0\) and solve for \( n \). This will give us the values of \( n \) where the function crosses the n-axis.

2. y-intercept: This occurs where \( n = 0 \). Substitute \( n = 0 \) into the function to find the corresponding \( g(n) \).

To find the n-intercepts, we set \( g(n) = 0 \): \[ -9(5n - 1)(4n + 1) = 0 \] This gives us two factors to solve:

1. \( 5n - 1 = 0 \) leads to \( n = \frac{1}{5} \)
2. \( 4n + 1 = 0 \) leads to \( n = -\frac{1}{4} \)

Thus, the n-intercepts are: \[ n = -\frac{1}{4} \quad \text{(smaller value)} \] \[ n = \frac{1}{5} \quad \text{(larger value)} \]

To find the y-intercept, we evaluate \( g(n) \) at \( n = 0 \): \[ g(0) = -9(5(0) - 1)(4(0) + 1) = -9(-1)(1) = 9 \] Thus, the y-intercept is: \[ g(0) = 9 \]

Final Answer