Question

How to find g(x) from parent function f(x)=2x-1 when the vertical translation is 4 units down

Answer 1

To find g(x) with a vertical translation of 4 units down from the parent function f(x)=2x-1, subtract 4 to get g(x)=2x-5.

Step-by-step explanation:

When determining the function g(x) derived from the parent function f(x) = 2x - 1 with a vertical translation of 4 units downward, the process involves subtracting 4 from the original function. Expressing the vertical translation mathematically, we use the formula g(x) = f(x) - k, where k represents the units of translation.

Here, with k = 4, the transformed function becomes g(x) = (2x - 1) - 4. By simplifying this expression, the final function is g(x) = 2x - 5. This approach illustrates how adjustments to the original function result in a modified function that reflects the desired vertical translation.

Answer 2

g(x), the new function, is shifted down 4 from the original f(x)=2x-1

Shifting down 4 is negative, so it would be subtracting 4 from the original

g(x)= 2x-1 -4

g(x) = 2x-5