Find the function whose graph is stretched horizontally

Question

Find the function whose graph is stretched horizontally
Find the function whose graph is stretched horizontally.(k > 1)
f(1kx)
1kf(x)
kf(x)
f(kx)

Answer 1

Actually, y=4x² is narrower than y=x²

 

If graphed, the 4, as the coefficient of x² multiplies the y value by 4, resulting in the following points:

 

y=4x²:  (0,0), (1,4), (-1, 4), (2, 8), (-2, 8);as opposed to the points for y=x²:  (0,0), (1,1),(-1,1),(2,4), (-2, 4).

 

Another way of thinking of this is "What happens when k is between 0 and 1."   The function become flatter, or the points become closer to the x-axis, thus getting wider.  Therefore the correct answer is k(f(x)), not f(kx).

 

So 4y = x²  becomes y = (1/4)x².

I hope this helps.

 

 

 

Answer 2

The parabola is stretched horizontally when the leading coefficient is less than 1

 

example:

 

f(x/2) = (1/4)x² is wider, or stretched horizontally compared to f(x) = x²

 

so the answer would be both 1kf(x) and kf(x)