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Vertical and horizontal translations of the graph of a function

# Vertical and horizontal translations of the graph of a function

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Vertical and horizontal translations of the graph of a function The graph of (in blue) is translated a whole number of units horizontally and vertically to obtain the graph of (in red). The function is defined by . Write down the expression for . When a graph is translated , each of its points is shifted the same distance in the same direction. Horizontal translations of a graph: When is shifted units to the right , we get the graph of . When is shifted units to the left , we get the graph of . More So, a positive shift (to the right) leads to subtraction, and a negative shift (to the left) leads to addition.

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Unformatted text preview: Vertical translations of a graph: When is shifted units upward , we get the graph of . When is shifted units downward , we get the graph of . More The current problem: The graph of is shifted units to the right and units downward to obtain the graph of . When is shifted units to the right, we get the graph of . When this graph is then shifted units downward, we get the graph of . This is the graph of . In other words, . We are given that , and so . For additional explanation, see your textbook: • Section 2.4: Transformations of Functions The answer is ....
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