Questions: Given the function f(x)=4x, which equation represents the function that is stretched by a factor of 3 and shifted 2 down? g(x)=3x+2 g(x)=3x-2 g(x)=12x+2 g(x)=12x-2

Given the function f(x)=4x, which equation represents the function that is stretched by a factor of 3 and shifted 2 down?
g(x)=3x+2
g(x)=3x-2
g(x)=12x+2
g(x)=12x-2

Transcript text: Given the function $f(x)=4 x$, which equation represents the function that is stretched by a factor of 3 and shifted 2 down? $g(x)=3 x+2$ $g(x)=3 x-2$ $g(x)=12 x+2$ $g(x)=12 x-2$

Solution

Solution Steps

Step 1: Understand the Transformation

The original function is $ f(x) = 4x $. We need to apply two transformations to this function:

Stretch the function by a factor of 3.
Shift the function 2 units down.

Step 2: Apply the Stretch Transformation

To stretch the function by a factor of 3, we multiply the entire function by 3. Thus, the new function becomes: \[ g(x) = 3 \cdot f(x) = 3 \cdot 4x = 12x \]

Step 3: Apply the Shift Transformation

Next, we shift the function 2 units down. This means we subtract 2 from the function: \[ g(x) = 12x - 2 \]