We are given function f(x) = 25x^2 -2.
g(x) is a vertical stretch of f(x) by a factor of 2.
We know, the transformation rule
y= k f(x), vertical stretch by a factor k. For k>0.
Because function f(x) is being vertical stretched by a factor of 2. So, we need to multiply f(x) function by 2.
Therefore, g(x) = 2 f(x) = 2*(25x^2-2).
Therefore, g(x) = 2*(25x^2-2) or g(x) = 50x^2-4.
Answer:
The Given function is
f(x)= 25 x² -2
Now, a function g(x) is obtained when the function f(x) is stretched by a factor of 2.
Consider point (x,y) on f(x).When function is stretched vertically by a factor of 2 ,it means, the coordinate changes from (x,y) to (x,2 y).
Since we have to stretch the function as whole, we will multiply original function by 2.
So, g(x)= 2× [25 x² - 2] =50 x² -4
g(x)=50 x²- 4
