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

Answer:

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

Step-by-step explanation:

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

The given function is

$f(x)=\frac{2}{3}(3x+1)-6x$

We can rewrite this function

$f(x)=\frac{2}{3}(3x+1)-6x\\f(x)=\frac{2}{3}(3x)+\frac{2}{3}-6x=2x-6x+\frac{2}{3}\\ f(x)=-4x+\frac{2}{3}$

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

$f(x)=-4x+\frac{2}{3}\\-4x+\frac{2}{3}=0\\-4x=-\frac{2}{3}}\\ x=\frac{2}{12} =\frac{1}{6}$

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

y-intercept is when x = 0

$f(x)=-4x+\frac{2}{3}\\f(0)=-4(0)+\frac{2}{3}=\frac{2}{3}$

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

Therefore,

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