SOLUTION: Given f(x) =x^2. Write the resulting function g(x) that is there obtained by taking f(x) and compressing it horizontally by a factor of 1/2 and then reflecting it over the y-axis.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Given f(x) =x^2. Write the resulting function g(x) that is there obtained by taking f(x) and compressing it horizontally by a factor of 1/2 and then reflecting it over the y-axis.       Log On


   

Question 1177625: Given f(x) =x^2. Write the resulting function g(x) that is there obtained by taking f(x) and compressing it horizontally by a factor of 1/2 and then reflecting it over the y-axis.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!


f%28x%29+=+x%5E2 compressed horizontally by a factor of 1%2F2 is
g%28x%29+=f+%28hx%29+
if 0%3Ch%3C1 the graph is stretched horizontally by a factor 1%2Fh
if h%3E1 the graph is compressed horizontally by a factor 1%2Fh
in your case
h=1%2F2+=>compressed horizontally by a factor 1%2Fh=1%2F%281%2F2%29=2
g%28x%29+=%282x%29%5E2
reflecting it over the y-axis:
The graph is reflected about the y-axis when f%28x%29=f%28-x%29.
Reflecting this function across the y-axis, we replace x by -x. Hence, the reflection across the y-axis is f%28-x%29=%28-x%29%5E2=x%5E2, nothing changes
Therefore, the reflection is the same as the original function.

g%28x%29+=%28-2x%29%5E2


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2%2C+%28-2x%29%5E2%29+