Answer:
New function is: [tex]g(x)=3x[/tex]
Step-by-step explanation:
Given:
The parent function given is:
[tex]f(x)=x[/tex]
Now, as per transformation rules, if a graph is vertically stretched by a factor of 'C' such that 'C' is greater than 1, then the function rule is given as:
[tex]f(x)\to Cf(x)[/tex]
So, we multiply the given function by 'C' units to get the transformed function.
Here, [tex]f(x)=x[/tex] and [tex]C=3[/tex]
As 3 > 1, therefore, the equation of the new function is given as:
[tex]g(x)\to Cf(x)=3x\\g(x)=3x[/tex]
Therefore, the equation of the new function is 3 times the original function and is equal to [tex]g(x)=3x[/tex].
