Transformations

Given the curve of a given function y=f(x), you may be required to sketch transformations of the curve. Transformations can shift, stretch and flip the curve of a function.

y-transformations

A y-transformation affects the y coordinates of a curve. You can identify a y-transformation as changes are made outside the brackets of y=f(x).

• $f(x)\rightarrow f(x)+4$, this is a shift in y, the x coordinates are unaffected but all the y coordinates go up by 4.
• $f(x)\rightarrow f(x)-3$, this is a shift in y, the x coordinates are unaffected but all the y coordinates go down by 3.
• $f(x)\rightarrow 2f(x)$, this is a stretch in y, the x coordinates are unaffected but all the y coordinates are doubled.
• $f(x)\rightarrow -f(x)$, this is a flip in y, the x coordinates are unaffected but all the y coordinates are flipped across the x-axis.

x-transformations

x-transformations always behave in the opposite way to what is expected. They can identified when changes are made inside the brackets of y=f(x).

• $f(x)\rightarrow f(x+4)$, this is a shift in the x direction, the y coordinates are unaffected but all the x coordinates go to the left by 4, the opposite direction to what is expected.
• $f(x)\rightarrow f(x-3)$, this is a shift in the x direction, the y coordinates are unaffected but all the x coordinates go to the right by 3, the opposite direction to what is expected.
• $f(x)\rightarrow f(2x)$, this is a stretch in the x direction, the y coordinates are unaffected but all the x coordinates are halved, the opposite to what is expected.
• $f(x)\rightarrow f(-x)$, this is a flip in the x direction, the y coordinates are unaffected but all the x coordinates are flipped across the y-axis.

See Curve Sketching for some more practice questions on Transformations.