5. Common Mistakes to Avoid When Finding Domain and Range
Ignoring Restrictions
A lot of students forget about restrictions, like square roots and fractions (denominators).
For example, the function ( f(x) = \sqrt{x} ) only works for numbers that are zero or bigger. So, its domain is from zero to infinity: ([0, \infty)).
Not Thinking About Real-Life Situations
Sometimes, real-life situations can limit the domain.
For example, time cannot be negative. This means that when you’re using time in a function, you can’t have negative inputs.
Forgetting About Multiple Outputs
Students often think that a function can only have one output for each input.
But some functions, like circles, can have two outputs. So, keep this in mind when you’re working with them!
Overlooking Asymptotes
Functions with vertical or horizontal asymptotes (lines that the graph approaches but never touches) have special domains.
For instance, the function ( f(x) = \frac{1}{x} ) doesn't include zero, so its domain is ((- \infty, 0) \cup (0, \infty)).
Misreading the Graph
Always double-check the graph with your calculated domain and range.
This will help you spot any mistakes and make sure everything matches up.
5. Common Mistakes to Avoid When Finding Domain and Range
Ignoring Restrictions
A lot of students forget about restrictions, like square roots and fractions (denominators).
For example, the function ( f(x) = \sqrt{x} ) only works for numbers that are zero or bigger. So, its domain is from zero to infinity: ([0, \infty)).
Not Thinking About Real-Life Situations
Sometimes, real-life situations can limit the domain.
For example, time cannot be negative. This means that when you’re using time in a function, you can’t have negative inputs.
Forgetting About Multiple Outputs
Students often think that a function can only have one output for each input.
But some functions, like circles, can have two outputs. So, keep this in mind when you’re working with them!
Overlooking Asymptotes
Functions with vertical or horizontal asymptotes (lines that the graph approaches but never touches) have special domains.
For instance, the function ( f(x) = \frac{1}{x} ) doesn't include zero, so its domain is ((- \infty, 0) \cup (0, \infty)).
Misreading the Graph
Always double-check the graph with your calculated domain and range.
This will help you spot any mistakes and make sure everything matches up.