identify the roots and y - intercept of the function below. fill in the sign table and sketch a graph. your…
identify the roots and y - intercept of the function below. fill in the sign table and sketch a graph. your graph must accurately cross all known intercepts. $f(x)=(x + 5)(x + 2)^2(x - 1)(x - 3)$ identify the y - intercept of the function.
Answer
Explanation:
Step1: Recall y - intercept formula
The y - intercept of a function (y = f(x)) is found by setting (x = 0).
Step2: Substitute (x = 0) into the function
Given (f(x)=(x + 5)(x + 2)^{2}(x - 1)(x - 3)), when (x = 0), we have (f(0)=(0 + 5)(0+ 2)^{2}(0 - 1)(0 - 3)). First, calculate ((0 + 5)=5), ((0 + 2)^{2}=4), ((0 - 1)=-1), ((0 - 3)=-3). Then (f(0)=5\times4\times(-1)\times(-3)). (5\times4 = 20), and (20\times(-1)\times(-3)=60).
Answer:
60