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 (-∞, ∞)
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