Question

Determine if the graph is a function then state the domain and range.

Answer 1

Explanation

A function is a set of relation that doesn't have repetitive domain. If we want to know if a graph is function or not, we have to do the line test.

Line Test

1. Draw a vertical line. Make sure that a line passes through a graph.
2. See if a line intercepts a graph more than one point or just only one.

Result

If a line intercepts a graph more than one point, it is not a function.

However, if a line only intercepts a graph just one point, it is indeed a function.

The given graph from the question is a function because it passes line test.

Domain and Range

Domain is the set of all x-values, meaning we only focus on x-axis or x-value only.

Range is the set of all y-values. We only focus on y-value or y-axis for Range.

Determine Domain from Graph

We can simply say that the domain is from starting domain or x-coordinate point to end x-coordinate point. For example, if a graph starts at x = -4 and ends at x = 2, we can say that - 4<=x=2.

Determine Range from Graph

Similar to Domain except Range starts from the minimum value or point to the maximum point or value. For example if a graph starts at min point = 6 and max point = 9. We can say that 6<=y<=9.

From the graph, the domain starts from negative infinity to positive infinity. Meaning that x can be any numbers. Hence, the domain is set of all real numbers. For range, the minimum value is 0 and max value is positive infinity. Therefore we write y>=0.

Answer

$\begin{cases} x \in \mathbb{R} \\ y \geqslant 0 \end{cases}$

Domain is set of all real numbers.

Range is greater or equal to 0.