High School

Type the correct answer in the box. Use numerals instead of words.
The graphs of functions f and g are shown.
2-
f
44 8 12 16
2g
6
8
Function g is defined as g(x) = f(x) - c. What is the value of c?
The value of c is

Type the correct answer in the box Use numerals instead of words The graphs of functions f and g are shown 2 f44 8 12

Answer :

The calculated value of c in the graph is -3

From the question, we have the following parameters that can be used in our computation:

The functions f(x) and g(x)

In the graph, we can see that

  • f(x): The blue graph passes through the point (4, 1)
  • g(x): The red graph passes through the point (4, -2)

This means that one of the functions is translated to the other.

We are given that g(x) = f(x) - c

So, we take the function f(x) as the parent function

From the points listed above, we have the following equations:

f(4) = 1 and g(4) = -2

We are also given that

g(x) = f(x) - c

This can be rewritten as

g(4) = f(4) - c

By substituting the values of f(4) and g(4), the equation becomes

-2 = 1 - c

Collect the like terms

c = 1 + 2

When evaluated, we have

c = 3

This means that the value of c is 3 and this can be interpreted as the vertical difference between the functions f(x) and g(x) is 3