just think of this, The domain of a rational function consists of all the real numbers x except those for which the denominator is 0 . To find these x values to be excluded from the domain of a rational function, equate the denominator to zero and solve for x .
A. g(x) = 10f(x)
We know that both f and g have a single x-intercept at x=-10.
Therefore, when transforming f, we should not have any vertical/horizontal transformations as this will shift g away from the zero at x=-10.
For B, this is a horizontal translation of 10 units to the left.
For C, this is a vertical translation of 10 units upwards.
And for D, ths is a vertical translation of 10 units downwards.
Therefore, the only choice that does not represent a vertical/horizontal translation is A.
A is the f vertically strectched by a factor of 10.
This will not affect the zeros of f and g.
You can picture this using the parent parabola function y=x².
If we shift this vertically or horizontally, the zeros will obviously change.
However, any vertical shift such as y=2x², y=10x², or even y=100x², the zero will still remain at x=0.