View attachment 7894 I was great up until this example. how would I go about answering this one? The "if <3" and such, throws me off. Thank you!
This is a "piecewise" definition of a function. The function F(x) is defined differently for values in different parts of the domain.
F(x) = 2x - 5 if x < 3 tells us that for any value of x which satisfies x < 3, F(x) will be found using the definition F(x) = 2x - 5. So, for example, suppose we are asked to find F(-1). Since -1 < 3, we'll use the rule F(x) = 2x - 5. Substitute -1 for x: F(-1) = 2(-1) - 5, and do the arithmetic. F(-1) = -2 - 5, for F(x) = -7.
F(x) = x^2 - 3x + 1 if x > 3 tells us that for any value of x which satisfies x > 3, we'll use the rule F(x) = x^2 - 3x + 1. For example, suppose we are asked to find F(7). Since 7 > 3, we'll use this part of the rule for the value of F(x). F(7) = 7^2 - 3*7 + 1, or F(7) = 49 - 21 + 1, or F(7) = 28 + 1, or F(x) = 29.
Now, what if we are asked to find F(3)? We have a definition which tells us what to do if x > 3, and we have a definition which tells us what to do if x < 3. Since there is NO definition given for x = 3, we'd have to say that F(3) is undefined.....
I hope this helps you.
I was great up until this example. how would I go about answering this one? The "if <3" and such, throws me off. Thank you!