The table below shows several values of the function f. | x | f(x) | | :---: | :---: | | -3 | 8 | | -1 | 2 | | 1 | 5 | | 3 | -1 | The function g is defined by g(x) = f(x + 2). What is the value of g(-1)?

The table below shows several values of the function f. | x | f(x) | | :---: | :---: | | -… — SAT

The table below shows several values of the function $f$ .

The function $g$ is defined by $g(x) = f(x + 2)$ . What is the value of $g(-1)$ ?

To find the value of

g(-1)

, substitute

x = -1

into the equation

g(x) = f(x + 2)

, which yields

g(-1) = f(-1 + 2) = f(1)

. Looking at the table, when the input is

1

, the output of the function

f

5

. Therefore, the value of

g(-1)

5

Substitute the given input value of

-1

for

x

in the definition of

g(x)

g(-1) = f(-1 + 2)

To find

g(-1)

, we need to replace

x

with

-1

in the equation

g(x) = f(x + 2)

Simplify the expression inside the function notation.

g(-1) = f(1)

Performing the addition

-1 + 2

yields

1

Use the table to find the value of

f(1)

f(1) = 5

Looking at the row in the table where

x = 1

, the corresponding value of

f(x)

5

Function transformations and notation using tables