The graph of the function f in the xy-plane passes through the point (5, -2). The function… — SAT

The graph of the function $f$ in the $xy$ -plane passes through the point $(5, -2)$ . The function $g$ is defined by $g(x) = f(x) + 6$ . Which of the following points must lie on the graph of $g$ ?

A
$(5, -8)$
B
$(11, -2)$
$(5, 4)$ Answer
D
$(-1, -2)$

Answer

The point

(5, 4)

Since the point

(5, -2)

is on the graph of

f

, we know that

f(5) = -2

. The function

g

is defined by

g(x) = f(x) + 6

, which represents a vertical shift upward by

6

units. Substituting

x = 5

into the equation for

g

yields

g(5) = f(5) + 6 = -2 + 6 = 4

. Therefore, the point

(5, 4)

must be on the graph of

g

Step-by-Step Solution

Determine the value of

f(5)

using the given point on the graph of

f

f(5) = -2

Since the point

(5, -2)

lies on the graph of

f

, the input

x = 5

corresponds to the output

y = -2

Use the definition of

g(x)

to evaluate

g(5)

g(5) = f(5) + 6 = -2 + 6 = 4

Substitute

x = 5

into the definition

g(x) = f(x) + 6

to find the corresponding

y

-value for the graph of

g

Key Concept

Vertical translations of function graphs

Estimated Time:45s

Question

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Step-by-Step Solution

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