Question

The graphs of f(x) and g(x) are shown below.

Answer 1

Answer:

On a coordinate plane, a straight line with a positive slope goes through points (negative 2, negative 6), (0, 0), and (2, 6).

Step-by-step explanation:

The function is given by f(x) = - x and another function is given by g(x) = 2x.

Now, (g - f)(x) will be given by

(g - f)(x) = 2x - (- x) = 3x .......... (1)

Now, we have to choose from the options of the graphs that is applicable to function (1).

So, on a coordinate plane, a straight line with a positive slope goes through points (negative 2, negative 6), (0, 0), and (2, 6). (Answer)

Answer 2

Answer:

Option C

Step-by-step explanation:

We are given that

$f(x)=-x$

The line passing through the points (0,0),(-6,6) and (6,-6).

$g(x)=2x$

The line passing through the points (-3,-6),(0,0) and (3,6).

We have to find the graph of (g-f)(x).

$(g-f)(x)=g(x)-f(x)=2x-(-x)=2x+x$

$(g-f)(x)=3x$

Substitute x=0

$(g-f)(0)=3(0)=0$

$(g-f)(2)=3(2)=6$

$(g-f)(-2)=3(-2)=-6$

$(g-f)(-6)=3(-6)=-18$

Option C is true.