Question

If you horizontally stretch the quadratic function, f(x)=x2, by factor of 4, what is the equation of the new function?

Answer 1

For this case, the parent function is given by:
 $f (x) = x ^ 2$
 We apply the following transformation:
 Expansions and horizontal compressions:
 The graph of y = f (bx):
 If 0 <b <1, the graph of y = f (x) expands horizontally by the factor of 1 / b. (It lengthens)
 Applying the transformation we have:
 $f (x) = ( \frac{1}{4} x) ^ 2$
 Therefore, the stretch factor is 4, due to:
 $\frac{1}{b} = \frac{1}{\frac{1}{4} }$
 Rewriting:
 $\frac{1}{b} = 4$
 Answer:
 the equation of the new function is:
 $f (x) = ( \frac{1}{4} x) ^ 2$