Question

the function \\(f(x)\\) is shown in the graph.

describe the effect of the translation \\(h(x) = f(x + 4)\\) on \\(f(x)\\).

• the function \\(f(x)\\) is translated 4 units to the right to form \\(h(x)\\).
• the function \\(f(x)\\) is translated 4 units to the left to form \\(h(x)\\).
• the function \\(f(x)\\) is translated 4 units upward to form \\(h(x)\\).
• the function \\(f(x)\\) is translated 4 units downward to form \\(h(x)\\).

Explanation:

Identify the transformation rule

$$ h(x) = f(x + c) $$

Apply the horizontal translation rule

Using the Function Transformations knowledge point:

$$
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$$

Match with the correct option

$$ \text{The function } f(x) \text{ is translated 4 units to the left to form } h(x). $$

Answer:

• The function \(f(x)\) is translated 4 units to the right to form \(h(x)\).
• The function \(f(x)\) is translated 4 units to the left to form \(h(x)\). (Correct answer)
• The function \(f(x)\) is translated 4 units upward to form \(h(x)\).
• The function \(f(x)\) is translated 4 units downward to form \(h(x)\).