Question

drag the points to create a graph that satisfies the following requirements:
domain: $-4,2$
range: $0,4$

Explanation:

Step1: Identify domain bounds

The domain is $[-4, 2]$, so the graph must start at $x=-4$ and end at $x=2$, with no points outside this $x$-interval.

Step2: Identify range bounds

The range is $[0, 4]$, so the graph must reach a minimum $y$-value of $0$ and a maximum $y$-value of $4$, with all $y$-values between these two.

Step3: Plot key points

1. Place a point at $(-4, 0)$ (left end, minimum range value)
2. Place a point at $(2, 4)$ (right end, maximum range value)
3. Add a point at $(0, 2)$ (midpoint, to connect the two ends and ensure all $y$-values between 0 and 4 are covered, or alternatively, plot a curve that goes from $(-4,0)$ up to $(-1,4)$ then down to $(2,0)$—any continuous or non-continuous graph that stays within $x \in [-4,2]$ and $y \in [0,4]$ works).

Answer:

A valid graph will have all its points within the $x$-interval $[-4, 2]$ and $y$-interval $[0, 4]$, with at least one point at $x=-4$, one at $x=2$, one at $y=0$, and one at $y=4$. For example, a line connecting $(-4, 0)$ to $(2, 4)$, or a curve that goes from $(-4,4)$ down to $(2,0)$, or a piecewise graph that covers the required domain and range.