If the graph of y = f(x) contains the point (3, 7), and the function g is defined by g(x) … — SAT

If the graph of $y = f(x)$ contains the point $(3, 7)$ , and the function $g$ is defined by $g(x) = f(x + 4) - 2$ , what is the value of $g(-1)$ ?

Answer: 5

Since the graph of

y = f(x)

contains the point

(3, 7)

, we have

f(3) = 7

. The function

g

is defined as

g(x) = f(x + 4) - 2

. To find the value of

g(-1)

, we substitute

x = -1

into the definition of

g

g(-1) = f(-1 + 4) - 2 = f(3) - 2

. Substituting

f(3) = 7

gives

g(-1) = 7 - 2 = 5

Translate the point

(3, 7)

on the graph of

f(x)

into function notation.

f(3) = 7

By definition, if a point

(a, b)

is on the graph of

y = f(x)

, then

f(a) = b

Substitute

x = -1

into the expression for

g(x)

to evaluate

g(-1)

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

To find

g(-1)

, replace every occurrence of

x

with

-1

in the function definition of

g(x)

Simplify the input of the function

f

and compute the final value.

g(-1) = f(3) - 2 = 7 - 2 = 5

Simplify

-1 + 4

3

, then substitute the known value

f(3) = 7

and subtract

2

Evaluating a transformed function using function notation and given coordinate points.

Question