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

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.

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

$g(x)=a\times f(x)$

Here, it is vertically stretch by 7

so, we get

$g(x)=7\times -6x$

$g(x)=-42x$

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

$g(x)=-1\times -42x$

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