The equatiom y = f(x) only means y = an equation in x
Thankfully there are only 4 graph transformations to learn.
y = kf(x)
If k is more than 1 the original graph is stretched along the y-axis by multiplying the whole function by k.
i.e. y = f(x) becomes y = kf(x)
However, if k is less than 1 the graph is squashed down in the y-direction instead.
y = f(x) + a
This is where the whole graph is slid up or down the y-axis with no distortion, and it is achieved by simply adding a number onto the end of the equation.
y = f(x - a)
This is where the whole graph slides to the left or right and it only happens when you replace 'x' everywhere in th equation with 'x - a'.
Remember, if you want to go from y = f(x) to y = f(x - a) you must move the whole graph a distance 'a' in the +ve direction.
Therefore, if you want to go from y = f(x) to y = f(x + a) you must move the whole graph a distance 'a' in the -ve direction.
y = f(kx)
These also go the 'wrong way'.
When k is a multiplier it scrunches the graph up, but when k is a divider it stretches the graph out.