On a coordinate plane, a line with a 90-degree angle crosses the x-axis at (negative 4, 0), turns at (negative 1, 3), crosses the y-axis at (0, 2) and the x-axis at (2, 0).

Question

What is the range of the function on the graph?

all real numbers
all real numbers less than or equal to –1
all real numbers less than or equal to 3
all real numbers less than or equal to 0

Answer 1

To determine the range of the function on the given graph, we need to analyze the points and the structure of the lines connecting these points.

1. The line crosses the x-axis at \((-4, 0)\), then turns at \((-1, 3)\).
2. The line continues from \((-1, 3)\) and crosses the y-axis at \((0, 2)\).
3. It then crosses the x-axis again at \((2, 0)\).

This generates a piecewise function with two segments:

- **Segment 1** runs from \((-4, 0)\) to \((-1, 3)\).
- **Segment 2** runs from \((-1, 3)\) through \((0, 2)\) to \((2, 0)\).

Examining the y-values (which are the range of the function) within these segments:

- For Segment 1 \((-4, 0)\) to \((-1, 3)\): the y-value increases from 0 to 3.
- For Segment 2 \((-1, 3)\) to \((0, 2)\) to \((2, 0)\): the y-value starts from 3, decreases to 2 at ((0, 2)), and continues to decrease to 0 at \((2, 0)\).

**Range of the function:**
Each segment includes all y-values that the function hits, from its minimum to its maximum point. Here the y-values range:
- Minimum y-value: 0 (when \(x = -4\) and \(x = 2\))
- Maximum y-value: 3 (when \(x = -1\) and \(-1 \leq x < 0\))

By analyzing these points, it's clear that the entire range of y-values (from the lowest y to the highest y in each segment, without any gaps) is from 0 to 3.

Therefore, the correct range of the function on this graph is:

- All real numbers less than or equal to 3

Notice, however, the better specific interpretation is that it includes all y-values from a minimum to a maximum, precisely **[0, 3]**, but covers the whole span as "all real numbers less than or equal to 3" if limited to given choices.

So, the most specific answer given the multiple-choice options is:
- **All real numbers less than or equal to 3**.