52 [itex]\neq[/itex] 24, but F(5) = 52 - 1 = 24.cue928 said:Let F: [-2,5] --> R be function with rule F(x) = x^2 - 1. Show range of F = [-1,24].
I get that 5^2 = 25 - 1 = 24, but how does one get the lower bound of the range to be -1?
Just because you can't use a graph to show what you need to show, that's not a good reason to skip that step. A graph might help you understand the function you're working with. Your function describes a portion of a very simple geometric figure. It's not clear to me that you realize this.cue928 said:Understood but unfortunately I can't use the graph to show it. They want us to use the definition of set equality and range of a function to do it.
A function is a mathematical relationship between two sets of numbers, where each input has exactly one output. It can also be thought of as a rule that assigns each input value to a unique output value.
To prove that a relationship is a function, you must show that each input value has exactly one corresponding output value. This can be done by creating a table or graph of the relationship and checking that no input values have multiple output values. Another way is to use the vertical line test, where a vertical line is drawn through the graph and it should only intersect at one point for each input value.
A function's domain is the set of all possible input values for which the function is defined. It is often represented by the letter 'x' and can be numbers, variables, or other mathematical expressions.
A function's range is the set of all possible output values for the function. It is often represented by the letter 'y' and can be numbers, variables, or other mathematical expressions.
To find the range of a function, you can either create a table or graph of the function and list all the output values, or you can use algebraic methods such as finding the maximum and minimum values of the function. Additionally, if the function is given in equation form, you can use substitution to find specific output values.