The table below shows several values of the function f. | x | f(x) | | :---: | :---: | | -5 | 12 | | -3 | -2 | | -1 | 4 | | 3 | 18 | The function g is defined by g(x) = \frac{1}{2}f(x + 4) + 3. What is the value of g(-5)?

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 $g(x) = \frac{1}{2}f(x + 4) + 3$ . What is the value of $g(-5)$ ?

Answer: 5

The correct answer is 5.

To find the value of

g(-5)

, substitute

-5

for

x

in the definition of

g(x)

, which gives

g(-5) = \frac{1}{2}f(-5 + 4) + 3 = \frac{1}{2}f(-1) + 3

. According to the table,

f(-1) = 4

. Substituting this value into the expression yields

g(-5) = \frac{1}{2}(4) + 3 = 2 + 3 = 5

Substitute the input value into the function definition.

g(-5) = \frac{1}{2}f(-5 + 4) + 3 = \frac{1}{2}f(-1) + 3

To evaluate

g(-5)

, replace all occurrences of

x

with

-5

in the definition of

g(x)

Find the value of

f(-1)

from the table.

f(-1) = 4

The table provides specific input-output pairs for the function

f

. When the input is

-1

, the output is

4

Calculate the final value.

g(-5) = 2 + 3 = 5

Substitute

4

for

f(-1)

in the expression and simplify the terms.

Evaluating transformed functions using tabular data and applying horizontal translations, vertical compressions, and vertical translations.