SOLUTION: Let f(x)=-3x. The graph of f(x) is transformed into the graph of g(x) by a vertical stretch of 4 units and a translation of 4 units right. What is the equation for g(x)?

Algebra ->  Graphs -> SOLUTION: Let f(x)=-3x. The graph of f(x) is transformed into the graph of g(x) by a vertical stretch of 4 units and a translation of 4 units right. What is the equation for g(x)?       Log On


   

Question 1099141: Let f(x)=-3x. The graph of f(x) is transformed into the graph of g(x) by a vertical stretch of 4 units and a translation of 4 units right.
What is the equation for g(x)?
Found 2 solutions by ikleyn, josmiceli:
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
g(x) = 4*f(x-4) = 4*(-3(x-4)) = 4*(-3x + 12) = - 12x + 48.


Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+f%28x%29+=+-3x+
The vertical stretch means that every +f%28x%29+ is
now going to to be 4 times bigger, so,
+f%28x%29+=+4%2A%28+-3x+%29+
+f%28x%29+=+-12x+
--------------------
If I subtract +4+ from +x+, then every previous x+
must moves to the right ( get bigger )
--------------------
+f%28x%29+=+-12%2A%28+x+-+4+%29+
+f%28x%29+=+-12x+%2B+48+
-------------------------
Here's a plot for original and 2 changes:
+graph%28+400%2C+400%2C+-8%2C+8%2C+-20%2C+20%2C+-3x%2C+-12x%2C+-12x+%2B+48+%29+