Question

On a coordinate plane, a curved line crosses the y-axis at (0, 1), crosses the x-axis at (.25, 0), turns at point (2, negative 3), and crosses the x-axis (3.75, 0).
What is the range of the function on the graph?

all the real numbers
all the real numbers greater than or equal to 0
all the real numbers greater than or equal to 2
all the real numbers greater than or equal to –3

Answer 1

To determine the range of the function based on the given points and behavior on the coordinate plane, let's analyze the information provided:

1. The function crosses the y-axis at (0, 1).
2. The function crosses the x-axis at (0.25, 0).
3. The function has a turning point at (2, -3).
4. The function crosses the x-axis again at (3.75, 0).

From this, we can infer several things:
- At (0, 1), the function value is 1.
- At the x-intercepts (0.25, 0) and (3.75, 0), the function value is 0.
- At the turning point (2, -3), the function reaches its minimum value of -3.

Given that the function turns at (2, -3), this suggests that at (2, -3), the function changes direction. Since the coordinate (2, -3) represents the lowest point in the range, the function value decreases to -3 and then increases again beyond this point.

Considering all these points, we can conclude that the range of the function includes all values from -3 to positive infinity. There are no values less than -3 in the range of the function.

Thus, the correct range of the function based on the graph described is:
**All the real numbers greater than or equal to -3.**