Question

For the piecewise Function below, which of the following statments is true? Someone please help me

Answer 1

The first one and the third one are correct. because for the when you plug 1 on the first piece wise function you get 3.

f(3) =1. and f(1)=3 so f(1)>f(3)

Answer 2

Remark

Let's just figure out what f(1) and f(3) are and what equation to use.

f(1)

f(1) is defined by the top condition. Look at the condition carefully. -3 ≤ x ≤ 1

So the value of f(1) is

(x + 1)² -1

(1 + 1)² - 1

2² - 1

4 - 1 = 3

f(3)

f(3) is governed by the middle condition. 1 < x ≤ 3

The value of f(3) is - x + 2 = - 3 + 2 = - 1

Conclusion

f(1) > f(3)

Comment

Both f(1) and f(3) are defined. You just have to look around to find out where. D is wrong.

We calculated both f(1) and f(3). f(1) is larger than f(3) so that is your answer.