How can transformations alter the graph of a parent function?

Answer 1

OK, so let's call the parent function you're given f(x). There's a series of transformations a parent function can go through:

-f(x) = makes the parent function reflect over the x-axis

On the other hand, f(-x) = makes it reflect over the y-axis

f(x+a) = makes the parent function shift a units to the left

f(x-a) = makes the parent function shift a units to the right

f(x)+a = makes the parent function shift a units up

f(x)-a = makes the parent function shift a units down

f(ax) if x is a fraction like 1/2 , makes the parent function stretch by a factor of 2 (or multiply each x by 2)

f(ax) if x is a whole number (or fractions greater or equal to 1) like 2, makes the parent function compress by a factor of 2 (or divide each x by 2)

a*f(x) if x is a fraction like 1/2, makes the parent function get shorter by a factor of 2 (or divide each y by 2)

a*f(x) if x is a whole number (or fractions greater or equal to 1) like 2, makes the parent function get taller by a factor of 2 (or multiply each y by 2)

One way you can always tell what to do is that everything that is INSIDE the parentheses will be the OPPOSITE of what you think it should do. OUTSIDE the parentheses will do EXACTLY what you think it should do.

And when performing the transformations, start inside the parentheses first and then move outside. For example, f(x-2)+2; move the parent function first to the right 2 units and THEN move it up 2 units.