Question

Given f(x) and g(x) = k⋅f(x), use the graph to determine the value of k.

Answer 1

Answer: -3.

Step-by-step explanation:

We are given that : $g(x)=kf(x)$      (1)

It means that f(x) and g(x) are proportional.

[Equation of direct variation: y=kx , where k= proportionality constant.]

From the given graph ,

At x= -3 , f(x)=1 and g(x) =-3

Put value of x=-3 in (1) , we get

$g(-3)=kf(-3)$  

$\Rightarrow\ -3=k(1)$  [∵ f(x)=1 and g(x) =-3]

$\Rightarrow\ -3=k$

i.e. The value of k = -3

Hence, the correct answer is -3.