Let g(x) be a horizontal shrink by a factor of 2/3, followed by a translation 4 units left of the graph of f(x)=√(6x). Write a rule for g(x) described by the transformations of the graph of f. I thought it was g(x)=√(4x+4) but maybe not, what is the correct answer and why?
+118667 Let g(x) be a horizontal shrink by a factor of 2/3, followed by a translation 4 units left of the graph of f(x)=√(6x). Write a rule for g(x) described by the transformations of the graph of f. I thought it was g(x)=√(4x+4) but maybe not, what is the correct answer and why?
\(f(x)=\sqrt{6x}\\ \text{Now shrink this by a factor of 2/3}\\ u(x)=\frac{2}{3}\sqrt{6x}\\ \text{Now move the graph 4 units in the negative direction}\\ g(x)=\frac{2}{3}\sqrt{6(x+4)}\)
Here are the graphs
They go green, orange, red (just like trapffic lights)
https://www.desmos.com/calculator/xndxrxb8uy
It will make your life easier, mathematically speaking, if you get these transformations all sorted in your head.
If you want, ask more questions about how it works :))
