Maths GCSE

Graphs - Shifts and Stretches overview.

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Function notation

The equatiom y = f(x) only means y = an equation in x

Thankfully there are only 4 graph transformations to learn.

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1. y-Stretch

y = kf(x)

If k is more than 1 the original graph is stretched along the y-axis by multiplying the whole function by k.

i.e. y = f(x) becomes y = kf(x)

However, if k is less than 1 the graph is squashed down in the y-direction instead.

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2. y-shift

y = f(x) + a

This is where the whole graph is slid up or down the y-axis with no distortion, and it is achieved by simply adding a number onto the end of the equation.

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3. x-Shift

y = f(x - a)

This is where the whole graph slides to the left or right and it only happens when you replace 'x' everywhere in th equation with 'x - a'.

Remember, if you want to go from y = f(x) to y = f(x - a) you must move the whole graph a distance 'a' in the +ve direction.

Therefore, if you want to go from y = f(x) to y = f(x + a) you must move the whole graph a distance 'a' in the -ve direction.

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4. x-Stretch

y = f(kx)

These also go the 'wrong way'.

When k is a multiplier it scrunches the graph up, but when k is a divider it stretches the graph out.

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