11. which description of transformations yields the
equation f(x) = |x +3| – 2 from its parent function
of f(x) = |x|?

includes: 1) a vertical shift downwards of "2" units, and 2) a horizontal shift to the left of 3 units.

Step-by-step explanation:

Let's recall the rules for transforming functions via horizontal and vertical shifts of their graphs, and pay particular attention at the operations involved in the transformation of the function leading to: .

We notice that the transformation added 3 units to the variable "x", and we also notice that there is a subtraction of 2 units to the full absolute value function. We therefore look for such changes in the list of vertical and horizontal shifts:

1) In order to shift the graph of a function vertically c units upwards, we must transform  f (x) by adding c to it.

2) In order to shift the graph of a function vertically c units downwards, we must transform  f (x) by subtracting c from it.

3) In order to shift the graph of a function horizontally c units to the right, we must transform the variable x by subtracting c from x.

4) In order to shift the graph of a function horizontally c units to the left, we must transform the variable x by adding c to x.

So we can conclude that the resulting function includes: 1) a vertical shift downwards of "2" units, and 2) a horizontal shift to the left of 3 units.

asnwer is (g o h o f)(x) = 2x - 6/x + 7

step-by-step explanation:

given,

f(x) = x - 3/x

g(x) = x + 3

h(x) = 2x + 1

we need to find : (g o h o f)(x)

we can write (g o h o f)(x) = g[ h{ f(x) } ]

so first we find h{f(x)}

h{f(x)} = f(x) + 3 = (x - 3/x) + 3

h{f(x)} = x - 3/x + 3

now we find g[ h{ f(x) } ].

g[ h{ f(x) } ] = g(x - 3/x + 3)       {plug h{f(x)} = x - 3/x + 3 in g[h{f(x)}] }

g(x - 3/x + 3) = 2 (x - 3/x + 3) + 1

                    = 2x - 6/x + 6 + 1

                    = 2x - 6/x + 7

hence we get (g o h o f)(x) = 2x - 6/x + 7