how will a vertical compression of the parent function y=x change the graph of the function? Write a new equation that represents this transformation.

Question

This is for my math class. We get ten bonus points if we know how to do it! I have no earthly idea of how to work it so help is welcome:))))

Answer 1

Hi Cecilia, try this

 

Draw a square with side, say 6, on an x-y plain (start at the origin (0,0) and 6 units to the right on x and six units up on y.

 

After you have your square imagine putting your hand on the line on top (y=6) and pushing it dawn. THAT IS THE PHYSICAL ASPECT OF VERTICAL COMPRESSION.

 

Here is it's mathematical aspect - what kind of number would you need to multiply to see the size shrinking? 6? 4? 1/4? 1/6?

 

As you may have been able to see multiplying by 6 and 4 stretches the length to 36 and 24 respectively, whereas multiplying by 1/4 and 1/6 shrinks (compresses) it to 1.5 unites and 1 unit respectively 

 

Therefore: compression is multiplying by a number less than 1

                stretching is multiplying by a number greater than 1

                multiplying by 1 doesn't change the function

 

compressed f(x) is k*f(x) where k,1

 

hope this helps