To find the x-intercepts (n-intercepts) and y-intercepts (g-intercepts) of the function g(n) = n(n+4)(n-7), we need to determine the values of n where the function crosses the x-axis (n-axis) and the value of g(n) when n is zero.
To find the x-intercepts (n-intercepts), we set g(n) equal to zero and solve for n. This means finding the values of n where g(n) crosses the x-axis. In this case, we set g(n) = 0:
n(n+4)(n-7) = 0
To find the values of n that satisfy this equation, we set each factor equal to zero and solve for n:
n = 0 (n-intercept)
n + 4 = 0 (n-intercept)
n - 7 = 0 (n-intercept)
Solving these equations, we find the n-intercepts:
n = 0, -4, 7
These values indicate the points where the graph of g(n) crosses the x-axis.
To find the y-intercept (g-intercept), we substitute n = 0 into the function g(n) and calculate the corresponding value:
g(0) = 0(0+4)(0-7) = 0
Therefore, the y-intercept (g-intercept) is 0.
In summary, the n-intercepts are at n = 0, n = -4, and n = 7, while the g-intercept is at g(0) = 0.