Let f(x) = |x|+ 5 The graph of f(x) is transformed into the graph of g(x) by a translation of 3 units left and a translation of 6 units up. What is the equation for g (x)?

g(x) = |x + 3| + 11

Step-by-step explanation:

Since we're doing the translation on function f(x), we can substitute x in g(x) as what is in f(x).

That basically means,

f(x + 3) + 6      -- it's x + 3 because we're going to the left. It's counter-intuitive. Positive is left, negative is right.

We can substitute f(x) as the values inside it to simplify.

|x + 3| + 5 + 6

|x + 3| + 11 = g(x)

7 ft 6 in means 7 1/2, because 6 in is 1/2 of a foot. 7 ft 8 in means 7 2/3 because 8 in is 2/3 of a foot. 23/3 = 7 2/3. 15/2 = 7 1/2.

23/3   *   15/2   = 57 1/2

step-by-step explanation:

(f - g)(x) = 5x^3 - 3

step-by-step explanation:

rearrange these functions vertically, with like terms in separate columns:

f(x) = 5x^3 - 2

g(x) =         +1

now subtract, column by column:

(f - g)(x) = 5x^3 - 3