Question

the graph of a quadratic function is shown below. identify the domain and range by moving the correct answer to each box. not all answers will be used. the domain of the function is
the range of the function is
options: $x\leq1$, $x\leq0$, $y\geq1$, $y\geq0$, $-2.25\leq x\leq1$, $0\leq y\leq5$

Explanation:

Step1: Determine the domain

The domain of a function is the set of all possible x - values. From the graph, we can see that the left - most point (the vertex) is at \(x=- 2.25\) (by looking at the grid, we can infer the x - coordinate of the vertex) and the right - most point (the blue dot) is at \(x = 1\). So the domain is the set of x - values from \(-2.25\) to \(1\), which can be written as \(-2.25\leq x\leq1\).

Step2: Determine the range

The range of a function is the set of all possible y - values. The vertex of the parabola (the minimum point since it opens upwards) has a y - coordinate of \(0\), and as we move along the graph, the y - values go up to \(5\) (from the graph's y - axis markings). So the range is the set of y - values from \(0\) to \(5\), which can be written as \(0\leq y\leq5\).

Answer:

The domain of the function is \(-2.25\leq x\leq1\).
The range of the function is \(0\leq y\leq5\).