What are the x and y intercepts? f(x) = ((x - 3)(x + 4)(x - 1))/((x + 2)(x - 12)) ​

Question

What are the x and y intercepts?


`f(x) = ((x - 3)(x + 4)(x - 1))/((x + 2)(x - 12))`
​

Answer 1

(a)The x-intercepts are 3, -4 and 1.

(b)f(x)=-0.5

Explanation:

Given the function:

`f(x) = ((x - 3)(x + 4)(x - 1))/((x + 2)(x - 12))`

• The x-intercepts occurs when y=0
• The y-intercepts occurs when x=0

x-Intercepts

When y=f(x)=0

`f(x) = ((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`

The x-intercepts are 3, -4 and 1.

y-intercepts

When x=0

`f(x) = ((x - 3)(x + 4)(x - 1))/((x + 2)(x - 12))\\f(x) = ((0 - 3)(0 + 4)(0 - 1))/((0 + 2)(0 - 12))\\= ((- 3)( 4)( - 1))/(( 2)( - 12))\\= (12)/(-24)\\\\=-0.5`

The y-intercept is -0.5