Subjects algebra

Function Shift

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1. **Problem Statement:** We are given a function $g$ which is a transformation of another function $t$. The graph of $g$ is shifted horizontally right by 1 unit compared to $t$. We need to find the formula for $g$ in terms of $t$. 2. **Understanding Horizontal Shifts:** A horizontal shift of a function $t(x)$ by $h$ units is represented as $t(x - h)$ if the graph shifts to the right, and $t(x + h)$ if the graph shifts to the left. 3. **Applying the Rule:** Since $g$ is shifted right by 1 unit, the formula for $g$ is: $$g(x) = t(x - 1)$$ 4. **Explanation:** The input to $t$ is adjusted by subtracting 1, which means every $x$ value in $g$ corresponds to $x-1$ in $t$. This shifts the graph to the right by 1 unit. 5. **Final Answer:** $$\boxed{g(x) = t(x - 1)}$$