BEWARE! THIS IS HARD!!
NOTE: f(x) just means an equation like y = something x. It’s not something to be scared by!
There are a few ways you might be asked to transform graphs.
y Shift: y = f(x) + a
Adding or subtracting a number to the end of the equation just moves the graph up or down.
- Red line is y = sin x
- Blue line is y = (sin x) + 3
- Green line is y = (sin x) – 1
x Shift: y = f(x + a)
This is where you replace x everywhere in the equation with (x + a)
Anything you do to x you must now do to (x + a). So if before you had x2 you would now replace it with (x + a)²
If a is positive you shift the graph to the left. If a is negative you shift it to the right. BE CAREFUL because this is probably the opposite of what you would expect instinctively.
- Red line is y = x²
- Yellow line is y = (x + 2)²
y Stretch: y = kf(x)
This involves multiplying the whole function by a number.
If k is greater than one then it stretches the graph parallel to the y axis. If it is less than 1 is squashes the graph parallel to the y axis.
x Stretch: y = f(kx)
For this one you replace all the values of x with x multiplied or divide by k.
If k is a multiplier it scrunches up the graph parallel to the x axis.
If k is a divider it stretches the graph.
Beware this is again probably counter intuitive!
- Red line is y = sin(x)
- Blue line is y = sin(2x)
Reflections: y = -f(x) and y = f(-x)
These are quite easy….just remember:
- To get y = -f(x) you just flip y = f(x) in the x axis
- To get y = f(-x) you just flip y = f(x) in the y axis