Mathematics

Question

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

2 Answer

  • B. g(x) = 42
    A flip over the x-axis means you flip the sign. A stretch means you multiply the factor of stretch to the coefficient.
  • Answer:

    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.




NEWS TODAY