Question

If you vertically stretch the linear parent function, Fx) = x, by multiplying by 3,

what is the equation of the new function?

Answer 1

New function is:
`g(x)=3x`

Explanation:

Given:

The parent function given is:

`f(x)=x`

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:

`f(x)\to Cf(x)`

So, we multiply the given function by 'C' units to get the transformed function.

Here,
`f(x)=x` and
`C=3`

As 3 > 1, therefore, the equation of the new function is given as:

`g(x)\to Cf(x)=3x\\g(x)=3x`

Therefore, the equation of the new function is 3 times the original function and is equal to
`g(x)=3x`.