Given g(x) = -x + 3, solve for x when g(x) = -1.
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Answer: B. [–4, 0) ∪ [2, ∞)
To find the range, find out what y-values are possible for the function in the graph.
<h2>Symbols</h2>We need to pay attention to what symbols to use.
<h3>Reading the diagram</h3>Solid circle
- The function touches the point.
Empty circle
- The function gets close, but does not touch the point.
Arrow
- The function keeps going to infinity.
Square brackets: [ and ]
- These show that the function touches the point.
Curved brackets: ( and )
- These show that the function gets close but does not touch the point.
- Infinity always uses a curved bracket.
Union of sets: ∪
- This symbol shows that sets of values are talking about the same thing. It's almost like the word 'and'.
Let's start by looking for the lowest possible y-value at the bottom of the diagram. On the graph, the point (4, –4) marked with a solid circle.
The function touches the point and stops. Since the y-value is –4, the lowest possible y-value is:
If we follow the blue line upwards, we find an empty circle at (0, 0). The y-value in (0, 0) is 0. This means that the function gets close, but does not include:
So, the first part of our range is:
- [–4, 0)
The blue line on the top starts where y = 2 at a solid circle. So, the function includes the y-value:
If we follow this blue line upwards, it ends with an arrow. This means it will keep going to infinity, which is the symbol:
So, the second part of our range is:
- [2, ∞)
Put the lower and upper blue lines together with the union of sets symbol. The range is expressed as: [–4, 0) ∪ [2, ∞)
Learn more about domain and range here: