Question

Using the graph f(x)=x^2 as a guide, describe the transformation and then graph each function

h(x)=(x-2)^2+2

h(x)=-(3x)^2

h(x)=(1/2x)^2

Answer 1

start describing

Answer 2

?

Answer 3

I dont understand.

Answer 4

f(x) = x^2
f(x-2)^2 = (x-2)^2 moves the graph f(x)=x^2 to the RIGHT by 2 units because we are replacing x by (x-2) in the function.
Then adding 2 to the right hand side moves the function UP by 2 units.

So, h(x) = (x-2)^2 + 2, moves the function f(x) = x^2 to the right by 2 units and then up by 2 units.

Answer 5

can you help with the other two?

Answer 6

b) h(x) = -(3x)^2
f(x) = x^2
f(3x) = (3x)^2
h(x) = -f(3x)
f(3x) compresses the graph f(x) horizontally by a factor of 3.
-f(3x) reflects the graph f(3x) about the x-axis.

Therefore, h(x) = -(3x)^2, first compresses the graph f(x) = x^2 horizontally by a factor of 3 and then reflect the graph about the x-axis.

I will let you finish the last question.

Also see http://www.regentsprep.org/regents/math/algtrig/ATP9/funclesson1.htm

Answer 7

Thank you.