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The required expressions for the domains and ranges of the given graphs are;

  • The range of the quadratic function of a graph is [1, ∞)
  • The domain of the quadratic function is (-∞, ∞)

The reasons why the above values for the range and domain are correct are;

The given vertex of the quadratic equation = (-2, 1)

The vertex form of a quadratic equation is y = a·(x - h)² + k

A point on the graph is (-1, 4)

Therefore;

4 = a·((-1) - (-2))² + 1 = a + 1

a = 4 - 1 = 3

The equation of the graph is y = 3·(x + 2)² + 1

The  domain and range expression having round brackets indicates that the adjacent values are not included. A square bracket means they are included.

  • The Range of the Function:

The range of the of the function of the graph having the equation y = 3·(x + 2)² + 1, and from the graph is found as follows;

The minimum y- value = 1

The maximum y-value = ∞ (infinity)

The range of the graph is 1 ≤ y ≤ ∞, which gives;

The range of the quadratic function of the graph is [1, ∞)

  • The Domain of the Function:

The graph of the function is U-shaped and the ends of the graph of the function extends to infinity on both sides

The domain of a function is the set of x-values that the function can have

From y = 3·(x + 2)² + 1, the possible x-values are -∞ < x < ∞

Therefore;

The domain of the quadratic function is (-∞, ∞)

Learn more about domain and range here:

https://brainly.com/question/19819428

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