Question

to solve the equation |x-9|=0.5x, kiana graphed the functions f(x)=|x-9| and g(x)=0.5x on the same set of coordinate axes. She then found that the graphs intersected at the points (6,3) and (18,9). Finally, she concluded that the solutions of the equation |x-9|=0.5x are x=6 amd x=18. which of the following reasons best justifies Kiana's conclusion.

Answer 1

Answer:

The answer is the option D

$f(6)=g(6)$ and $f(18)=g(18)$

Step-by-step explanation:

we have

$f\left(x\right)=\left|x-9\right|$

$g(x)=0.5x$

we know that

The solution of the system of equations is the intersection point both graphs

Using a graphing tool

see the attached figure

The solution are the points $(6,3)$ and $(18,9)$

therefore

The solution of the equation $\left|x-9\right|=0.5x$ are

$x=6, x=18$

so

For $x=6$

$f\left(6\right)=\left|6-9\right|=3$

$g(6)=0.5(6)=3$

$f(6)=g(6)$

For $x=18$

$f\left(18\right)=\left|18-9\right|=9$

$g(18)=0.5(18)=9$

$f(18)=g(18)$

therefore

$f(6)=g(6)$ and $f(18)=g(18)$ because the intersection points are common points for both graphs

Answer 2

Answer:

Option: D is the correct answer.

  F(6)=G(6)     and   F(18)=G(18)

Step-by-step explanation:

We know that the point of intersection of the graph of two function f(x) and g(x) is the set of possible x values at which both the function have the same output values.

i.e. if the graph of two functions intersect at x=a than that means:

                                 f(a)=g(a)

Hence, here the graph of F(x)=|x-9| and G(x)=0.5x intersect at x=6 and x=18 ,

this means that:

                F(6)=G(6)

      and    F(18)=G(18)