Question

Which statement correctly describes the relationship between the graph of f(x) and the graph of g(x)=f(x)−4 ?

The graph of g(x) is the graph of​​ ​ f(x) ​ translated 4 units down.

The graph of g(x) is the graph of f(x) translated 4 units left.

The graph of g(x) is the graph of ​​ f(x)​ translated 4 units up.

The graph of g(x) is the graph of ​ f(x)​ translated 4 units right.

Answer 1

See below

Explanation:

Just translate the graph of f(x) four units downward.

Answer 2

The graph of g(x) is the graph of​​ ​ f(x) ​ translated 4 units down.

Explanation:

Parent graph = f(x)

Translated graph = g(x)=f(x)-4

Rule : When the graph of f(x) is shift downward by b units

So, f(x)→f(x)-b

So, on comparing the equation of resultant graph with rule

b = 4

So, the Graph f(x) is translated 4 units down to obtain g(x)

So, Option A is true.

Hence The graph of g(x) is the graph of​​ ​ f(x) ​ translated 4 units down.