Question

Which statement is true regarding the graphed functions? A) f(4)=g(4) B) f(4)=g(-2) C) f(2)=g(-2) D) f(-2)=g(-2)

Answer 1

Option (D)

Explanation:

If the two points
`(x_1,y_1)` and
`(x_2,y_2)` are lying of the line.

Slope of the line represented by the function 'f' =
`(y_2-y_1)/(x_2-x_1)`

Two points are lying on the line are (-2, 4) and (0, -2).

Slope of the line passing through these points 'm' =
`(4+2)/(-2-0)`

m = -3

Y-intercept of the line 'b' = -2 [From the graph]

Therefore, equation of the function will be,

f(x) = (-3)x - 2

f(x) = -3x - 2

Similarly, for other function represented by the line in red,

Slope of the line passing through (-6, 0) and (0, 6) =
`(6-0)/(0+6)`

m' = 1

Y-intercept of g(x) = 5 [From the graph]

Equation that represents the function g(x) = 1.x + 5

g(x) = x + 5

For g(x) = f(x)

-3x - 2 = x + 6

-3x - x = 2 + 6

-4x = 8

x = -2

Therefore, for x = -2 both the functions will have the value.

f(-2) = g(-2)

Option (D) will be the answer.