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.

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jimrgrant1 jimrgrant1 · Answer 1 · 2019-09-25T14:48:58+02:00

Answer:

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

joaobezerra joaobezerra · Answer 2 · 2021-10-19T12:15:06+02:00

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

D. It is the graph of [tex]y = \ln{x}[/tex] translated 3 units up and 7 units to the right.

The parent function is:

[tex]f(x) = y = \ln{x}[/tex]

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

[tex]f(x - 7) = \ln{(x - 7)}[/tex]

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

[tex]f(x - 7) + 3 = \ln{(x - 7)} + 3[/tex]

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 https://brainly.com/question/18405655