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).

• Upward shift: , this is a shift in y. The x coordinates are unaffected but all the y coordinates go up by 4.
• Downward shift: , this is a shift in y. The x coordinates are unaffected but all the y coordinates go down by 3.
• Vertical stretch: , this is a stretch in y. The x coordinates are unaffected but all the y coordinates are doubled.
• Reflect in x-axis: , 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 be identified when changes are made inside the brackets of y=f(x).

• Left shift: , 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.
• Right shift: , 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.
• Shrink in x: , 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.
• Reflect in y-axis: , this is a flip in the x direction. The y coordinates are unaffected but all the x coordinates are flipped across the y-axis.

Note that y-transformations usually behave as expected as opposed to x-transformations that seem to do the opposite.

See Curve Sketching for some more practice questions on Transformations.

JOKE: I’ll do algebra, geometry, trigonometry and probability…. but graphing is where I draw the line.

More graph jokes. 🙂

Also see other Things to Remember.