The graph of g is given below. Sketch the graph of the following functions. Try to be as accurate as possible and explain how you got your answers.

Question

The graph of g is given below. Sketch the graph of the following functions. Try to be as accurate as possible and explain how you got your answers.

1. Sketch g(x+1)+2.
2. Sketch -g(x)
3. Sketch 3g(x)
4. Sketch g(12x)

Answer 1

Hi,

first make a name for all special point such as:

A (-2,0) B(-1, 1) C(0,0) D(2,2) E(4,0)

1. Sketch g(x+1)+2.

Must all above points go 1 unit to the left and 2 units up then connect these points

It means: A (-2,0) ---> (-3,2)

B(-1, 1) ---> (-2,3)

C(0,0) -----> (-1,2)

D(2,2) ----> (0,4)

E(4,0) -----> (2,2)

2-Sketch -g(x)

Must all y of points times negative

It means:

A (-2,0) ---> (-2,0)

B(-1, 1) ---> (-1,-1)

C(0,0) -----> (0,0)

D(2,2) ----> (2,-2)

E(4,0) -----> (4,0)

connect to each new points it will be -g(x)

3-Sketch 3g(x)

looks like # 2 all y of points times 3 and no change x of points

4- g(12x)

must x of all points equal 12 then solve equation till find x of new points dont change y

It means:

A (-2,0) ---> -2 = 12x ----> x = -1/6----> (-1/6,0)

B(-1, 1) ---> -----> (-1/12, 1)

C(0,0) -----> (0,0)

D(2,2) ----> (1/6,-2)

E(4,0) -----> (1/3,0)

I hope it is useful,

Minoo