Transformations of graphs Summary of the four types of transformation

Y = f(x) is any function or equation of a graph. This example is an cubic function/equation. y = f(x) There are five basic types of transformation of a graph i.e. five ways we can move the graph or change its shape

Point (x, y) becomes point (x, y+a) y = f(x) + a y = f(x) +a Point (x, y) becomes point (x, y+a) y = f(x) + a This is a ‘shift’ in the y-direction

Point (x, y) becomes point (x-a, y) y = f(x) y = f(x+a) -a Point (x, y) becomes point (x-a, y) y = f(x+a) This is a ‘shift’ in the x-direction, opposite to the sign of number a

y = f(x) y = -f(x) y = -f(x) This is a ‘reflection’ in the axis, mirror line y = 0 Every y coordinate gets multiplied by -1

y = Af(x) y = f(x) Notice what happens at the zeros y = Af(x) This is a ‘stretch’ in the y-direction, Scale factor A. Every answer (y-coordinate) gets multiplied by A

Notice what happens at the y-intercept y = f(Ax) y = f(x) y = f(Ax) This is a ‘stretch’ in the x-direction, Scale factor 1/A Every x coordinate gets multiplied by 1/A, y values stay the same

One missing transformation What about f(-x) f(x)=x3-3x-1 Reflection across the y axes