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)?

Answer 1

g(x) = 42x

Explanation:

Start with the function f(x) = -6x.

If we stretch it vertically by a factor of 7, f(x) becomes g(x) = 7(-6x) = -42x.

If we now reflect this g(x) in the x-axis, the rule becomes g(x) = 42x.

Answer 2

we are given a function

`f(x)=-6x`

First translation:

The graph of function is vertically stretched by a factor of 7

Whenever we vertically stretch any function by 'a' units

so, we can write it as

`g(x)=a* f(x)`

Here, it is vertically stretch by 7

so, we get

`g(x)=7* -6x`

`g(x)=-42x`

Second translation:

Whenever we reflect any function about x-axis

we multiply y-value by -1

so, we can write it as

`g(x)=-f(x)`

Here , it is reflected in the x-axis

so, we can multiply by -1 to y-value

we get

`g(x)=-1* -42x`

`g(x)=42x`.............Answer