When students learn about domain and range for functions, they often make a few common mistakes. Here are some of those mistakes and how to avoid them:
Not Looking for Restrictions: Many students forget to check for numbers that can’t be used, like when you divide by zero. For example, in the function ( f(x) = \frac{1}{x-2} ), you can’t use ( x = 2 ) because it makes the function undefined. So, ( x = 2 ) is not part of the domain.
Overlooking Limits: Some students don't realize that not all functions can go off to infinity in both directions. For example, a parabola like ( f(x) = x^2 ) starts at 0 and goes up, but it doesn't go down to (-\infty). So, in this case, the range starts at 0.
Mixing Up Domain and Range: It’s easy to confuse these two ideas! Just remember this: the domain is all the possible ( x ) values you can use, and the range is all the possible ( y ) values.
Taking a little extra time to look over the function can really help clear up these mistakes!
When students learn about domain and range for functions, they often make a few common mistakes. Here are some of those mistakes and how to avoid them:
Not Looking for Restrictions: Many students forget to check for numbers that can’t be used, like when you divide by zero. For example, in the function ( f(x) = \frac{1}{x-2} ), you can’t use ( x = 2 ) because it makes the function undefined. So, ( x = 2 ) is not part of the domain.
Overlooking Limits: Some students don't realize that not all functions can go off to infinity in both directions. For example, a parabola like ( f(x) = x^2 ) starts at 0 and goes up, but it doesn't go down to (-\infty). So, in this case, the range starts at 0.
Mixing Up Domain and Range: It’s easy to confuse these two ideas! Just remember this: the domain is all the possible ( x ) values you can use, and the range is all the possible ( y ) values.
Taking a little extra time to look over the function can really help clear up these mistakes!