How to do this? (#21 and #23)

the graph of g is a transformation of the graph of f. write a rule for g.

Step-by-step explanation:

f(x) + n - shift the grapf n units up

f(x) - n - shift the grapf n units down

f(x + n) - shift the grapf n units to the left

f(x - n) - shift the grapf n units to the right

-f(x) - reflection about the x-axis

f(-x) - reflection about the y-axis

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Look at the picture.

move the graph 2 units to the right and 1 unit up

move the graph 4 units down

reflection the graph about the X axis.

21. g(x) = f(x-1); 23. g(x) = -ƒ(x)  

Step-by-step explanation:

21. ƒ(x) = log₃x

The graph is shifted one unit to the right.

One unit must have been subtracted from x.

g(x) = -f(x-1) = log₃(x-1)

Figure 1 shows ƒ(x) (blue) and g(x) (green) shifted one unit to the right,

23.

The graph is inverted.

ƒ(x) must have been multiplied by -1.

g(x) = -ƒ(x)

Figure 2 shows ƒ(x) (purple) and g(x) = -ƒ(x) (black).