The function f(x) = -6x. the graph of g(x) is f(x)vertically stretched by a factor of 7 and reflected in the x-axis. what is the function rule for g(x)?

a. g(x) = -6/7x

b. g(x) = 42x

c. g(x) = -42x

d. g(x) = 6/7x

option: B( g(x)=42 x)

Step-by-step explanation:

We are given a function f(x)= -6 x

Now the graph of g(x) is:  " f(x) vertically stretched by a factor of 7 and reflected in the x-axis" .

( we know that for any function f(x) the graph g(x) which is a vertical stretch by a factor 'a' is given by:

h(x)=a f(x)

now as the function is then reflected in the x-axis this means that the resultant function is given by:

g(x)= -h(x)  )

So here we are given a vertical stretch by a factor  '7'

⇒ h(x)=7 f(x)=7×(-6)x= -42 x

also now this function is reflected in the x-axis

Now the resultant function g(x) is given by:

g(x)= -h(x)

⇒ g(x)=42 x

Hence, option B is correct.