Which expression represents translating f(x) to the left by 4 units?

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Study for the Algebra 1 Honors End-of-Course Test. Study with flashcards and multiple-choice questions, each question has hints and explanations. Get ready for your exam!

Multiple Choice

Which expression represents translating f(x) to the left by 4 units?

Explanation:
Horizontal shifts come from the sign inside the function’s argument. If you replace x with x − h, the graph moves to the right by h; if you replace x with x + h, it moves to the left by h. To move f(x) left by 4 units, you use x + 4 inside, giving g(x) = f(x + 4). The other forms do something different: f(x) − 4 shifts the graph down 4 units, f(−x) reflects the graph across the y-axis, and f(−x) + 4 would reflect and then move up, not shift left.

Horizontal shifts come from the sign inside the function’s argument. If you replace x with x − h, the graph moves to the right by h; if you replace x with x + h, it moves to the left by h. To move f(x) left by 4 units, you use x + 4 inside, giving g(x) = f(x + 4). The other forms do something different: f(x) − 4 shifts the graph down 4 units, f(−x) reflects the graph across the y-axis, and f(−x) + 4 would reflect and then move up, not shift left.

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