determine the number of x - intercepts that appear on a graph of each function.\n$f(x)=(x + 1)(x - 3)(x…
determine the number of x - intercepts that appear on a graph of each function.\n$f(x)=(x + 1)(x - 3)(x - 4)$\n$f(x)=(x + 5)^3(x - 9)(x + 1)$\n$f(x)=(x - 6)^2(x + 2)^2$\n$f(x)=(x + 2)(x - 1)x-(4 + 3i)x-(4 - 3i)
Answer
Explanation:
Step1: Recall x - intercept concept
The x - intercepts of a function (y = f(x)) are found by setting (f(x)=0).
Step2: Analyze (f(x)=(x + 2)(x - 1)[x-(4 + 3i)][x-(4 - 3i)])
Set (f(x)=0). Then ((x + 2)(x - 1)[x-(4 + 3i)][x-(4 - 3i)] = 0). Using the zero - product property (ab = 0) implies (a = 0) or (b = 0), we have: (x+2=0\Rightarrow x=-2), (x - 1=0\Rightarrow x = 1), (x-(4 + 3i)=0\Rightarrow x=4 + 3i), (x-(4 - 3i)=0\Rightarrow x=4 - 3i). But complex roots do not appear on the graph of a real - valued function (y = f(x)) (where (x,y\in R)). Only real roots contribute to x - intercepts on the graph. The real roots are (x=-2) and (x = 1).
Answer:
2