The graph of the function f in the xy-plane is translated 4 units to the right and 3 units… — SAT

The graph of the function $f$ in the $xy$ -plane is translated $4$ units to the right and $3$ units down to create the graph of the function $g$ . Which of the following equations defines $g(x)$ in terms of $f(x)$ ?

A
$g(x) = f(x + 4) - 3$
B
$g(x) = f(x - 4) + 3$
$g(x) = f(x - 4) - 3$ Answer
D
$g(x) = f(x + 4) + 3$

Answer

The equation that defines

g(x)

in terms of

f(x)

g(x) = f(x - 4) - 3

The equation

g(x) = f(x - 4) - 3

correctly represents the translated function. A translation of

4

units to the right is represented by replacing

x

with

x - 4

within the function's input, and a translation of

3

units down is represented by subtracting

3

from the outer function.

Step-by-Step Solution

Apply the horizontal translation to the function input.

f(x - 4)

Translating a function

f(x)

horizontally to the right by

h

units is represented by substituting

x

with

x - h

. For a shift of

4

units to the right, we replace

x

with

x - 4

Apply the vertical translation to the function output.

f(x - 4) - 3

Translating a function vertically down by

k

units is represented by subtracting

k

from the entire function. For a shift of

3

units down, we subtract

3

Write the final equation for

g(x)

g(x) = f(x - 4) - 3

Combining the horizontal and vertical transformations yields the function

g(x)

Key Concept

Graph transformations of functions

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

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