Question

Write the equation of the graph obtained when the graph of y -

is compressed vertically by a factor of 0.25, translated 4 units
right, and then translated 3 units up.

Answer 1

Answer: y = 0.25*f(x - A) + 3

Explanation:

Initially we have the graph of y = f(x)

If we do a vertical compression, this means that we multiply the function by the scale factor, in this case the scale factor is 0.25

So now our graph is y = 0.25*f(x)

A translation to the right by A units means that now we valuate the function in x - A, in this case A = 4, so our graph now is:

y = 0.25*f(x - 4)

A vertical translation means that we add a constant to the function, if the constant is positive the tranlsation is upwards, if the constant is negative the translation is downwards.

Here the translation is of 3 units upwards, so our new graph is:

y = 0.25*f(x - A) + 3