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

On a coordinate plane, a straight line with negative a slope represents f (x) = negative x. The line goes through points (0, 0), (negative 6, 6) and (6, negative 6). On a coordinate plane, a straight line with a positive slope represents g (x) = 2 x. The line goes through points (negative 3, negative 6), (0, 0) and (3, 6).

Which of the following is the graph of (g – f)(x)?
On a coordinate plane, a straight line with a negative slope goes through points (negative 2, 6), (0, 0), and (2, negative 6)
On a coordinate plane, a straight line with a negative slope goes through points (negative 6, 6), (0, 0), and (6, negative 6).
On a coordinate plane, a straight line with a positive slope goes through points (negative 2, negative 6), (0, 0), and (2, 6).
On a coordinate plane, a straight line with a positive slope goes through points (negative 6, negative 6), (0, 0), and (6, 6).

1 Answer

4 votes

Answer:

Option C

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.

The graphs of f(x) and g(x) are shown below. On a coordinate plane, a straight line-example-1
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