Question

HELPP PLEASE GIVE EVIDENCE

Given a graph for the transformation of f(x) in the format g(x)=f(x)+k determine the k value
Answer Options:
k=-3
k=3
k=5
k=8

Answer 1

See vertex has same x

• Vertex of f(x)=(-3,-3)
• Vertex of g(x)=(-3,5)

So

Put the values in equation

• g(x)=f(x)+k
• g(-3)=f(-3)+k
• 5=-3+k
• k=5+3
• k=8

Option D

Answer 2

Explanation:

The value of k in the equation g(x) = f(x) + k comes out to be 8.

How the vertical shifting of a graph takes place?

If the graph of a function f(x) is shifted vertically by k units, f(x) becomes f(x)+k.

From the diagram, we can say that graph of f(x) has been shifted vertically by 8 units

If we shift f(x) vertically by 8 units f(x) becomes f(x)+8 and also coincides with the graph of g(x).

So, g(x) = f(x) + 8........(1)

Comparing (1) and g(x) = f(x) + k, we get k=8.

Hence, the value of k in the equation g(x) = f(x) + k comes out to be 8.