Answer:
Given any function f(x), substitute x=0 into the function to find the y-intercept.
Explanation:
The y-intercept of any function is the value of y at which the function crosses the y-axis.
At that point where it crosses the y-axis, the corresponding value of x=0.
So, given any function f(x), substitute x=0 into the function to find the y-intercept.
As an illustration, we use the two given examples:
(a)f(x)=(x+1)(x-3)(x-4)
Let x=0
[tex]\begin{gathered} f\mleft(x\mright)=\left(x+1\right)\left(x-3\right)\left(x-4\right) \\ f(0)=(0+1)(0-3)(0-4) \\ =1\times-3\times-4 \\ f(0)=12 \end{gathered}[/tex]
The coordinates of the y-intercept is (x,y)=(0,12).
(b)y=(x-2)²(x+3)
[tex]\begin{gathered} y=(x-2)^2(x+3) \\ \text{ When x=0} \\ y=(0-2)^2(0+3)=(-2)^2\times3=4\times3=12 \end{gathered}[/tex]
The coordinates of the y-intercept is (x,y)=(0,12).
