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Which of the following transformations would result in a vertical shift of the g

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Question: Which of the following transformations would result in a vertical shift of the graph of the function f(x) = x^2?

Options:

  1. f(x) = x^2 + 3
  2. f(x) = 3x^2
  3. f(x) = x^2 - 3
  4. f(x) = 2x^2

Correct Answer: f(x) = x^2 + 3

Solution: 

Adding a constant to the function, such as f(x) = x^2 + 3, results in a vertical shift upwards.

Which of the following transformations would result in a vertical shift of the g

Practice Questions

Q1
Which of the following transformations would result in a vertical shift of the graph of the function f(x) = x^2?
  1. f(x) = x^2 + 3
  2. f(x) = 3x^2
  3. f(x) = x^2 - 3
  4. f(x) = 2x^2

Questions & Step-by-Step Solutions

Which of the following transformations would result in a vertical shift of the graph of the function f(x) = x^2?
  • Step 1: Start with the original function, which is f(x) = x^2.
  • Step 2: Understand that a vertical shift means moving the graph up or down.
  • Step 3: To shift the graph upwards, add a positive constant to the function, like f(x) = x^2 + 3.
  • Step 4: To shift the graph downwards, subtract a constant from the function, like f(x) = x^2 - 2.
  • Step 5: Recognize that adding or subtracting a constant changes the height of the graph without changing its shape.
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