Question

Consider the function f(x) = √(x) Write down the new function g(x) which results from scaling f(x) vertically by a factor of 1/4 and scaling horizontally by a factor of 1/2 g(x)=

Answer 1

The new function g(x) after scaling f(x) = √(x) vertically by 1/4 and horizontally by 1/2 is g(x) = 1/4 √(2x). This includes a vertical multiplication of the function values by 1/4 and horizontal scaling by multiplying x by 2 before taking the square root.

Step-by-step explanation:

To obtain the new function g(x) after scaling the function f(x) = √(x) vertically by a factor of 1/4 and horizontally by a factor of 1/2, we need to apply the respective transformations accordingly.

For vertical scaling by a factor of 1/4, we multiply the output (function values) by 1/4. This transformation gives us 1/4 √(x).

For horizontal scaling by a factor of 1/2, we need to multiply the input (x-value) by the reciprocal of the scale factor, which is 2 in this case. So the input to the square root becomes (2x) instead of x, giving us a transformed function √(2x).

Combining both transformations, we get the new function g(x) = 1/4 √(2x), which involves applying both the vertical and horizontal scaling to f(x).