Ohio Educators Math Exam Practice 2025 – Complete Prep Guide

Question: 1 / 400

In the context of transformations, what does subtracting from the input (f(x±k)) do?

Horizontal shift left

Subtracting from the input in a function, represented as f(x ± k), results in a horizontal shift of the graph of that function. Specifically, when you subtract a positive constant k (f(x - k)), the entire graph shifts to the right by k units. Conversely, if you add a positive constant (f(x + k)), it shifts to the left by k units. This is because the input value must reach a larger value to produce the same function output; thus, the graph moves accordingly.

This transformation is key to understanding how functions behave under shifts and changes, which is crucial in both algebra and calculus. By mastering this concept, students can easily analyze and graph functions in various contexts.

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Vertical shift up

Vertical shift down

Horizontal shift right

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