Question

Describe how to transform the graph of g(x)=ln x into the graph of f(x)=ln(x-4)+3

a.
Translate 4 units to the left and 3 units up
c.
Translate 4 units to the right and 3 units down
b.
Translate 4 units to the right and 3 units up
d.
Translate 3 units to the left and 4 units down

Answer 1

The answer is because it says 4 units to the right the right is always the + x-axis so we must take the opposite sign so ( x-4) -4 is on the negative x axis so we take + side and say it goes in the + direction to the right. It is 3 units up because what ever we have outside the bracket is for the y-axis and it's +.

Answer 2

Translate 4 units to the right and 3 units up.

Explanation:

Given : translation of the graph of g(x)=ln x to obtain the graph of f(x)=ln(x-4)+3.

To find : Which of the following describes the translation of the graph.

Solution : We have given that

Parent function g(x)=ln x

Translated function f(x)=ln(x-4)+3

By the translation rule : f(x) →→→→→→ f(x-h) it mean function shifted right by h unit

f(x) →→→→→→ f(x)+k it mean function shifted up by k unit.

Since , graph of g(x)=ln x function shifted right by 4 unit and function shifted up by 3 unit.

Therefore, Translate 4 units to the right and 3 units up.