Begin by graphing the standard absolute value function f(x) = | x |. Then use transformations of this graph to describe the graph the given function.
h(x) = 2 | x | + 2
f(x) = |x| is a V with point at origin and 45 degrees up in quadrants 1 and 2
move the whole thing up 2
and double the slopes
try some points
(0,0) ---> (0,2)
(1,1) ---> (1,4)
(-1,1) --> (-1,4) etc
when do i stop ?
1,1 ---> 1,6
1,1 1,8
2,2 2,4
no
the point (1,1)
becomes
y = 2 |1| + 2 = 4 period, not 6
in other words (1,4)
Oh so the answer is (1,1) .. How can I describe it ? cause it says "Then use transformations of this graph to describe the graph the given function. "
the point (2,2) (y must = x)
becomes
y = 2 |2| + 2 = 6 (y must equal 2 x+2)
so
(1,2) in the old graph becomes (1, 6)
etc
The new graph has a point at (0,2), not at (0,0)
The new graph has slopes of 2 and -2 instead of 1 and -1
in other words translate up[ 2 and double the slopes of the V shape