. how to sketch the graph

f(x) = |x-4| + 2

|a| ≥ 0 ∀ a∈R

That means the minim of the function will be when |x-4|=0 ⇒ x = 4

f(4) = |4-4|+2

f(4) = 2 ⇒ M(4,2) - minim point

We notice that the function f is ascending for x ∈ [4,+∞) and is descending for x ∈ (-∞,4]

Because the function is linear,the sketch of the graph will be 2 lines with the intersection in the point M(4,2) (in our case).

Let's find f(0) = |0-4|+2 = 4+2 = 6 ⇒ N (0,6) is the intersection of the function with Oy axis. (now we can sketch the graph only for x ∈(-∞,4] )

Now let's calculate the function for a value bigger than 4 : for example f(5) = 3 ⇒ P (5,3) ∈ Gf

So you can see the graph in the picture.Have a nice day :)

hurricanes form when warm, moist air from the ocean surface quickly rises into the atmosphere and forms storm clouds and rain. when the clouds are formed, heat is released which warms the cool air in the upper regions of the atmosphere so that the cycle can continue. which two phases of the water cycle are repeated in this process?