SOLUTION: Given the equation {{{ y=2^x }}} predict the equation for the graph that has been reflected in the y-axis, given a vertical stretch by a factor of 5, translated 2 units right and 5

Algebra ->  Graphs -> SOLUTION: Given the equation {{{ y=2^x }}} predict the equation for the graph that has been reflected in the y-axis, given a vertical stretch by a factor of 5, translated 2 units right and 5      Log On


   

Question 1098461: Given the equation +y=2%5Ex+ predict the equation for the graph that has been reflected in the y-axis, given a vertical stretch by a factor of 5, translated 2 units right and 5 units down
Found 2 solutions by josmiceli, ikleyn:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
1st the original graph and the graph
translated 2 units right and 5 units down
+y+=+2%5Ex+
+y+%2B+5+=+2%5E%28+x+-+2+%29+
+graph%28+400%2C400%2C+-10%2C+10%2C+-10%2C+10%2C+2%5Ex%2C+2%5E%28+x-2+%29+-+5++%29+
--------------------------
Reflected about the y-axis:
+y+=+2%5E%28-x-2%29+-+5+
+graph%28+400%2C400%2C+-10%2C+10%2C+-10%2C+10%2C+2%5E%28+-x-2+%29+-+5++%29+
---------------------------
vertical stretch by factor of +5+:
+y+=+5%2A2%5E%28+-x-2+%29+-+5+
+graph%28+400%2C+400%2C+-10%2C+10%2C+-10%2C+10%2C+5%2A2%5E%28+-x-2+%29+-+5++%29+
--------------------------------
Definitely feel free to get another opinion on this

Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
.
Given the equation +y=2%5Ex+ predict the equation for the graph that has been reflected in the y-axis,
given a vertical stretch by a factor of 5, translated 2 units right and 5 units down
~~~~~~~~~~~~~~~~~ 

y = 2%5Ex.

Reflected in the y-axis:                     y = 2%5E%28-x%29;


given a vertical stretch by a factor of 5:   y = 5%2A2%5E%28-x%29;


translated 2 units right:                    y = 5%2A2%5E%28-%28x-2%29%29;


             and 5 units down:               y = 5%2A2%5E%28-%28x-2%29%29+-+5.


Answer:  y = 5%2A2%5E%28-%28x-2%29%29+-+5,  or, equivalently,  y = 5%2A2%5E%28-x%2B2%29+-+5 = 5%2A%284%2A2%5E%28-x%29-1%29.