What is the effect on the graph of the function f(x) = x2 when f(x) is changed to 3f(x − 2)?

Answer 1

Grouping a number with the "x" equates to translating (or moving) the graph in the "x" direction. The only thing is that "x" is Mr. Opposite, so if you see a -2, then you are moving RIGHT by 2 units. So f(x - 2) moves f(x) = x² to the right by 2 units.

Multiplying the function by 3 equates to stretching f(x) in the "y" direction by 3. Note that the 3 is NOT grouped with the "x" so it will not affect the "x", it affects the "y". So 3f(x) stretches f(x) = x² by a factor of 3 in the "y" direction.

Putting these together, 3f(x - 2) will move the graph f(x) = x² to the right by 2 and stretch it in the "y" direction by a factor of 3.