linear transformation

Question

The graph of f(x)=x was translated down 21 units and right 5 units to create the graph of p(x)

Write the equation of p(x) using function notation.

Answer 1

Pushing the graph down by 21 means any point (x1,y1) will move to (x1,y1-21). This means

p(x) = f(x) - 21

Pushing the graph right by 5 means any point (x1,y1) will move to (x1+5, y1). This means

p(x) = f(x-5)

Combining both

p(x) = f(x-5) - 21 = (x-5) - 21 = x - 26

Answer 2

First....p(x) = f(x)-21

Then horizontal shifting to the right means that p(x) = x - 21 - 5 = x - 26

As a side note...You can determine which direction the horizontal shift goes by looking at it this way....(x - a) = (x - +a). The + indicates the direction of the actual shift. In the case of (x + a), then look at it this way....(x - - a), whereby the second "-" indicates a shift to the left.