When students start learning about domain and range in math, they often make some common mistakes. Here are a few I’ve noticed from my own experiences:
Overlooking restrictions: Sometimes, students forget about restrictions in rational functions. For example, in the function ( f(x) = \frac{1}{x-2} ), they might mistakenly think the domain is all real numbers. But ( x ) can't be 2, so they need to remember that!
Mixing up domain and range: This is a common confusion, especially when looking at graphs. Students might incorrectly identify values on the x-axis as part of the range instead of the domain, and the other way around too.
Not looking at the graph's shape: Some students forget to pay attention to how a graph behaves at both ends. For example, with ( f(x) = x^2 ), the graph reaches a lowest point but continues upward forever. This means the domain is all real numbers, or ((-∞, ∞)), while the range only includes positive numbers, or ([0, ∞)).
Ignoring notation: It’s really important to use the right symbols. Using brackets and parentheses correctly matters! For example, ( [a, b] ) means including the numbers a and b, while ( (a, b) ) means not including them. Many students get these mixed up.
Knowing about these common mistakes can really help improve understanding in this topic!
When students start learning about domain and range in math, they often make some common mistakes. Here are a few I’ve noticed from my own experiences:
Overlooking restrictions: Sometimes, students forget about restrictions in rational functions. For example, in the function ( f(x) = \frac{1}{x-2} ), they might mistakenly think the domain is all real numbers. But ( x ) can't be 2, so they need to remember that!
Mixing up domain and range: This is a common confusion, especially when looking at graphs. Students might incorrectly identify values on the x-axis as part of the range instead of the domain, and the other way around too.
Not looking at the graph's shape: Some students forget to pay attention to how a graph behaves at both ends. For example, with ( f(x) = x^2 ), the graph reaches a lowest point but continues upward forever. This means the domain is all real numbers, or ((-∞, ∞)), while the range only includes positive numbers, or ([0, ∞)).
Ignoring notation: It’s really important to use the right symbols. Using brackets and parentheses correctly matters! For example, ( [a, b] ) means including the numbers a and b, while ( (a, b) ) means not including them. Many students get these mixed up.
Knowing about these common mistakes can really help improve understanding in this topic!