Question
The graph of a quadratic function, f ,is shown on the grid. Which of these best represents the DOMAIN of, f.
Points on the graph: ( -3, 0), (4,0) , (0,-12) and (0.5, -12.25).
A: -4 ≤ x ≤ 5
B: y ≥ -12.25
C: All real numbers
D: All real numbers less than -4 or greater than 5
Points on the graph: ( -3, 0), (4,0) , (0,-12) and (0.5, -12.25).
A: -4 ≤ x ≤ 5
B: y ≥ -12.25
C: All real numbers
D: All real numbers less than -4 or greater than 5
Answers
GPT-4o mini
To determine the domain of the quadratic function \( f \), we need to identify the range of x-values for which the function f(x) is defined based on the given points.
The points on the graph are:
1. \((-3, 0)\)
2. \((4, 0)\)
3. \((0, -12)\)
4. \((0.5, -12.25)\)
From the points \((-3, 0)\) and \((4, 0)\), we can see that the graph of the quadratic function intersects the x-axis at \(x = -3\) and \(x = 4\). Since these two points are the x-intercepts, we know that the quadratic function is defined for values that fall between or outside these intercepts.
The quadratic function will be defined for all values of \(x\) in the range of real numbers from negative infinity to positive infinity.
Therefore, the best representation of the domain of \(f\) is:
**C: All real numbers**
This means that there are no restrictions on the x-values.
The points on the graph are:
1. \((-3, 0)\)
2. \((4, 0)\)
3. \((0, -12)\)
4. \((0.5, -12.25)\)
From the points \((-3, 0)\) and \((4, 0)\), we can see that the graph of the quadratic function intersects the x-axis at \(x = -3\) and \(x = 4\). Since these two points are the x-intercepts, we know that the quadratic function is defined for values that fall between or outside these intercepts.
The quadratic function will be defined for all values of \(x\) in the range of real numbers from negative infinity to positive infinity.
Therefore, the best representation of the domain of \(f\) is:
**C: All real numbers**
This means that there are no restrictions on the x-values.