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If the function g(x) = 2x + 3 is transformed to g(x) = 2(x - 1) + 3, what type o

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Question: If the function g(x) = 2x + 3 is transformed to g(x) = 2(x - 1) + 3, what type of transformation has occurred?

Options:

  1. Vertical shift up.
  2. Vertical shift down.
  3. Horizontal shift left.
  4. Horizontal shift right.

Correct Answer: Horizontal shift right.

Solution: 

The transformation g(x) = 2(x - 1) + 3 indicates a horizontal shift to the right by 1 unit.

If the function g(x) = 2x + 3 is transformed to g(x) = 2(x - 1) + 3, what type o

Practice Questions

Q1
If the function g(x) = 2x + 3 is transformed to g(x) = 2(x - 1) + 3, what type of transformation has occurred?
  1. Vertical shift up.
  2. Vertical shift down.
  3. Horizontal shift left.
  4. Horizontal shift right.

Questions & Step-by-Step Solutions

If the function g(x) = 2x + 3 is transformed to g(x) = 2(x - 1) + 3, what type of transformation has occurred?
  • Step 1: Start with the original function g(x) = 2x + 3.
  • Step 2: Look at the transformed function g(x) = 2(x - 1) + 3.
  • Step 3: Notice that inside the parentheses, x is replaced by (x - 1).
  • Step 4: Understand that replacing x with (x - 1) means we are shifting the graph horizontally.
  • Step 5: Since we are subtracting 1 from x, this indicates a shift to the right.
  • Step 6: Conclude that the transformation is a horizontal shift to the right by 1 unit.
  • Function Transformation – Understanding how changes in the function's equation affect its graph, specifically horizontal shifts.
  • Horizontal Shift – Recognizing that g(x) = 2(x - 1) + 3 represents a shift of the graph to the right by 1 unit.
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