To find g(x), we need to apply the transformations to the function f(x).

Step 1: Translate 12 units to the left.
This means we replace every x in the function with (x+12). So, f(x) becomes f(x+12) = 3| (x+12) - 5 | + 10.

Step 2: Simplify the expression inside the absolute value.
f(x+12) = 3| x + 7 | + 10.

Step 3: Translate 4 units up.
This means we add 4 to the entire function. So, f(x+12) becomes g(x) = 3| x + 7 | + 14.

So, the function g(x) which is the translation 12 units left and 4 units up of f(x) = 3|x–5|+10 is g(x) = 3| x + 7 | + 14.

Question

To find g(x), we need to apply the transformations to the function f(x).

Step 1: Translate 12 units to the left. 
This means we replace every x in the function with (x+12). So, f(x) becomes f(x+12) = 3| (x+12) - 5 | + 10.

Step 2: Simplify the expression inside the absolute value.
f(x+12) = 3| x + 7 | + 10.

Step 3: Translate 4 units up.
This means we add 4 to the entire function. So, f(x+12) becomes g(x) = 3| x + 7 | + 14.

So, the function g(x) which is the translation 12 units left and 4 units up of f(x) = 3|x–5|+10 is g(x) = 3| x + 7 | + 14.

Knowee AI · Accepted Answer

To find g(x), we need to apply the transformations to the function f(x).

Step 1: Translate 12 units to the left. 
This means we replace every x in the function with (x+12). So, f(x) becomes f(x+12) = 3| (x+12) - 5 | + 10.

Step 2: Simplify the expression inside the absolute value.
f(x+12) = 3| x + 7 | + 10.

Step 3: Translate 4 units up.
This means we add 4 to the entire function. So, f(x+12) becomes g(x) = 3| x + 7 | + 14.

So, the function g(x) which is the translation 12 units left and 4 units up of f(x) = 3|x–5|+10 is g(x) = 3| x + 7 | + 14.

Find g(x), where g(x) is the translation 12 units left and 4 units up of f(x)=3|x–5|+10.