To understand different types of breaks or "discontinuities" in math, let's look at them in simpler terms:
Jump Discontinuity: This is when a function suddenly changes its value. Think about the weather. The temperature can drop quickly from a warm 20 degrees Celsius during the day to a chilly 10 degrees Celsius at night. That's a jump!
Infinite Discontinuity: This happens when a function keeps going up without stopping. A good example is the function ( f(x) = \frac{1}{x} ). As we get closer to zero, this function rises higher and higher to infinity.
Removable Discontinuity: Imagine you have a hole in your function. This type of break happens when you can easily "fix" the hole. For example, the function ( f(x) = \frac{x^2 - 1}{x - 1} ) has a hole at ( x=1 ). But, if we change it a bit, we can fill that hole and make it work smoothly again.
By understanding these different types of breaks, we can look at functions more clearly!
To understand different types of breaks or "discontinuities" in math, let's look at them in simpler terms:
Jump Discontinuity: This is when a function suddenly changes its value. Think about the weather. The temperature can drop quickly from a warm 20 degrees Celsius during the day to a chilly 10 degrees Celsius at night. That's a jump!
Infinite Discontinuity: This happens when a function keeps going up without stopping. A good example is the function ( f(x) = \frac{1}{x} ). As we get closer to zero, this function rises higher and higher to infinity.
Removable Discontinuity: Imagine you have a hole in your function. This type of break happens when you can easily "fix" the hole. For example, the function ( f(x) = \frac{x^2 - 1}{x - 1} ) has a hole at ( x=1 ). But, if we change it a bit, we can fill that hole and make it work smoothly again.
By understanding these different types of breaks, we can look at functions more clearly!