What is the Range of a Function with Rule F(x) = x^2 - 1 on the Interval [-2,5]?

[cue928]

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?

 

[Mark44]

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?

5² $\neq$ 24, but F(5) = 5² - 1 = 24.

Sketch a graph of the function and you should be able to see why the minimum value in the range is -1.

 

[cue928]

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.

I understand that for two sets to be equal, A must be a subset of B and B must be a subset of A. For range of a function f from A to be, y is an element of B such for all x in A, x,y must both be elements of F. But I'm not making the connection between the two definitions and the question.

 

[daveb]

To test for maxima and minima, you look at the two points onthe end of the interval (-2 and 5 in this case), then look at where F'(x) = 0.

 

[SammyS]

How do you find the minimum of a function?

 

[Mark44]

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.

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.