Each statement describes a transformation of the graph of y = ln x. which statement correctly describes the graph of y = ln(x - 7) + 3? a. it is the graph of y = ln x translated 3 units up and 7 units to the left. b. it is the graph of y = ln x translated 7 units down and 3 units to the right. c. it is the graph of y = ln x translated 7 units up and 3 units to the right. d. it is the graph of y = ln x translated 3 units up and 7 units to the right.

Using translation concepts, it is found that the correct option is:

D. It is the graph of translated 3 units up and 7 units to the right.

The parent function is:

Shifting a function a units to the right is equivalent to finding f(x - a), thus:

Shifting a function a units up is equivalent to finding f(x) + a, thus:

Which means that the function was shifted 7 units to the right and 3 up, thus, option D is correct.

A similar problem is given at link

D

Step-by-step explanation:

Given f(x) then f(x + a) is a horizontal translation of f(x)

• If a > 0 then shift of a units left

• If a < 0 then shift of a units right

Given f(x) then f(x) + c is a vertical translation of f(x)

• If c > 0 then shift of c units up

• If c < 0 then shift of c units down

Hence y = ln(x - 7) + 3

Is the graph of y = lnx translated 3 units up and 7 units right → D

d

step-by-step explanation:

i used the pitagoras theoreme

- (2, -7)

- lines r and s and lines t and u must be parallel