Question

Sketch the linear function f(x) = 2/3(3x + 1) − 6x. Which key feature of the graph is true?

A) y-intercept (0,-4)
B) x-intercept (2/3,0)
C) x-intercept (1/6,0)
D) y-intercept (0,-1/3)

Answer 1

C) x-intercept (1/6,0)
1/6 = 0.167

Answer 2

C) x-intercept (1/6,0).

Explanation:

To find the right answer, we can find both axis interceptions.

The given function is

`f(x)=(2)/(3)(3x+1)-6x`

We can rewrite this function

`f(x)=(2)/(3)(3x+1)-6x\\f(x)=(2)/(3)(3x)+(2)/(3)-6x=2x-6x+(2)/(3)\\ f(x)=-4x+(2)/(3)`

So, x-intercept is when f(x) = 0

`f(x)=-4x+(2)/(3)\\-4x+(2)/(3)=0\\-4x=-(2)/(3)}\\ x=(2)/(12) =(1)/(6)`

This means that x-intercept points is (1/6, 0).

y-intercept is when x = 0

`f(x)=-4x+(2)/(3)\\f(0)=-4(0)+(2)/(3)=(2)/(3)`

y-intercept point is (0, 2/3).

Therefore,

the right choice is C) x-intercept (1/6,0).