SOLUTION: Transform the function f(x) as described and write the resulting function as an equation f(x)=x^2 Translate left 2 units stretch horizontally by a factor of 2 reflect over t

Algebra ->  Rational-functions -> SOLUTION: Transform the function f(x) as described and write the resulting function as an equation f(x)=x^2 Translate left 2 units stretch horizontally by a factor of 2 reflect over t      Log On


   

Question 1145166: Transform the function f(x) as described and write the resulting function as an equation
f(x)=x^2
Translate left 2 units
stretch horizontally by a factor of 2
reflect over the x-axis
stretch vertically by a factor of 3
translate up 4 units
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Transform the function f(x) as described and write the resulting function as an equation
f(x)=x^2
Translate left 2 units
stretch horizontally by a factor of 2
reflect over the x-axis
stretch vertically by a factor of 3
translate up 4 units
Start with 

f%28x%29=x%5E2 <--the red graph

graph%28400%2C400%2C-10%2C10%2C-10%2C10%2Cx%5E2%29
Translate left 2 units

replace x by (x+2)

g%28x%29+=+%28x%2B2%29%5E2 <--the green graph

graph%28400%2C400%2C-10%2C10%2C-10%2C10%2Cx%5E2%2C%28x%2B2%29%5E2%29
stretch horizontally by a factor of 2

Replace x by x/2

h%28x%29+=+%28x%2F2%2B2%29%5E2 <--the blue graph

graph%28400%2C400%2C-10%2C10%2C-10%2C10%2Cx%5E2%2C%28x%2B2%29%5E2%2C%28x%2F2%2B2%29%5E2%29
reflect over the x-axis

Multiply the whole right side by -1

k%28x%29=-%28x%2F2%2B2%29%5E2 <--the purple graph (it opens downward)
stretch vertically by a factor of 3

Multiply the whole right side by 3.

m%28x%29=-3%28x%2F2%2B2%29%5E2 <---the yelowish-green graph (opens downward)
translate up 4 units

Add +4 to the whole right side:

m%28x%29=-3%28x%2F2%2B2%29%5E2%2B4 <---the light blue graph.



Edwin