Question

The equation f(x) = |4x-3|+2 translated 2 units down is represented by which function: g(x)=?

a) g(x)=|4x-5|
b) g(x)=|4x-1|
c) g(x)=|4x-3|
d) g(x)=|4x-7|

Answer 1

The equation f(x) = |4x - 3| + 2 translated 2 units down is represented by the function c) g(x) = |4x - 3|.

Step-by-step explanation:

To translate the function f(x) = |4x - 3| + 2 downward by 2 units, you subtract 2 from the entire function. This vertical translation will only affect the constant term of the function since the constant term determines the vertical shift.

Here's the step-by-step process:

1. Start with the original function: f(x) = |4x - 3| + 2
2. To translate the function 2 units down, you subtract 2 from the function: f(x) - 2 = |4x - 3| + 2 - 2
3. Simplify the expression: g(x) = |4x - 3|

The resulting function g(x) should be equal to what you started with, minus the vertical shift. Since the vertical shift is -2, you only adjust the constant term. The absolute value part |4x - 3| remains unchanged.

Thus, the correct answer is:

c) g(x) = |4x - 3|