Question

The table for the quadratic functions f(x) and g(x) are given.

x f(x) g(x)
−4 16 4
−2 4 1
0 0 0
2 4 1
4 16 4

Determine the type of transformation and the value of k.
g of x equals one fourth time f of x
g of x equals f of one fourth times x
g(x) = 4f(x)
g(x) = f(4x)

Answer 1

Since g(x) = 1/4f(x), we have that g(x) is a horizontal stretch of f(x) by a factor of 4. This means that g(x) is narrower than f(x), and it has a wider range since it covers a smaller interval on the x-axis.

The value of k in this case is 0, since both f(0) and g(0) are equal to 0.

Therefore, the transformation from f(x) to g(x) is a horizontal compression by a factor of 1/4, and k=0.

Explanation:

Answer 2

g(x) = f(4x)

Explanation:

It worked for my test.