we are given a function
[tex]f(x)=-6x[/tex]
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
[tex]g(x)=a\times f(x)[/tex]
Here, it is vertically stretch by 7
so, we get
[tex]g(x)=7\times -6x[/tex]
[tex]g(x)=-42x[/tex]
Second translation:
Whenever we reflect any function about x-axis
we multiply y-value by -1
so, we can write it as
[tex]g(x)=-f(x)[/tex]
Here , it is reflected in the x-axis
so, we can multiply by -1 to y-value
we get
[tex]g(x)=-1\times -42x[/tex]
[tex]g(x)=42x[/tex].............Answer
Answer:
g(x) = 42x
Step-by-step 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.
