Answer:
(a)The x-intercepts are 3, -4 and 1.
(b)f(x)=-0.5
Step-by-step explanation:
Given the function:
[tex]f(x) = \dfrac{(x - 3)(x + 4)(x - 1)}{(x + 2)(x - 12)}[/tex]
- The x-intercepts occurs when y=0
- The y-intercepts occurs when x=0
x-Intercepts
When y=f(x)=0
[tex]f(x) = \dfrac{(x - 3)(x + 4)(x - 1)}{(x + 2)(x - 12)}=0\\(x - 3)(x + 4)(x - 1)=0\\x - 3=0$ or $ x + 4=0 $ or $ x - 1=0\\x=3$ or $ -4$ or $ 1[/tex]
The x-intercepts are 3, -4 and 1.
y-intercepts
When x=0
[tex]f(x) = \dfrac{(x - 3)(x + 4)(x - 1)}{(x + 2)(x - 12)}\\f(x) = \dfrac{(0 - 3)(0 + 4)(0 - 1)}{(0 + 2)(0 - 12)}\\= \dfrac{(- 3)( 4)( - 1)}{( 2)( - 12)}\\= \dfrac{12}{-24}\\\\=-0.5[/tex]
The y-intercept is -0.5
