Functions for math

Question

"Start with one of the parent functions f(x) = 1/x, f(x) = √x or f(x) = |x| and

a. write the transformed function if we shift f(x) left 2 units, stretch it vertically by a factor of 3 and shift down 4 units.


b. Given that the point (1,3) is on the graph of y=f(x), what are the coordinates of the point on the graph of the transformed function?"

 

I do not know where to begin with this problem. If someone could walk me through it, that would be great. Thanks!

Answer 1

I'll pick f(x) = √x for the example.  You can imitate the steps that I give below for the other functions.

 

So observe the graph of f(x). Its beginning point is (0,0) and it curves up through the first quadrant, in a downward concave manner, but y values always increase as x increases.

 

If the function is shifted left  units, then the beginning point of the curve moves along the x axis to -2.  This gives g(x) = √(x+2).  Observe that g(-2) = 0.

 

Next, vertical stretch by factor 3 gives us NEW g(x) = 3√(x+2).

 

Finally, downward shift by 4 units lowers all y values, giving FINAL g(x) = √(x+2) - 4.

 

Now you should be able to proceed on the other two functions, similarly.