Question

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Answer 1

Since x = 0 < 1, f(x) will be y = x2

Answer 2

Substitute x with 0

Answer 3

Why not?

Answer 4

For \(x\le1,~~\)you have \(f(\mathbf{\color{red}{x}}) = \mathbf{\color{red}{x}}^2\)

So \(f(\mathbf{\color{red}{0}}) = (\mathbf{\color{red}{0}})^2 = \cdots~?\)

Answer 5

No no. Since x = 0, you don't have to care about the case that x>1.

Answer 6

Because \(x = 0\), you will just go to case where \(x\le1\), because it is true that \(0\le1\)

In case \(x\le1\), you have \(f(x) = x^2\). Substitute x with 0 here. then you can evaluate \(f(0)\)

Answer 7

This function is divided into two cases.
1- When x > 1, then y = 2x +1. You won't care about y = x^2 when x > 1.
2- When x<=1, then y = x^2. At this time, you won't care about y = 2x + 1.

Answer 8

Exactly.

Answer 9

Yes. The answer is 0.

Answer 10

You can do it.

Answer 11

First, you draw the function y = x^2.

Answer 12

Then you will erase the right side of the graph from x = 1.

Answer 13

Instead, you will draw the function y = 2x + 1.

Answer 14

It is weird that the function is non-continuous. But this is how it looks anyway.

Answer 15

Actually, the left-side of the graph will be y = x^2 while the right-side will be y = 2x + 1

Answer 16

Yes, they are positive: 3 and 1

Answer 17

This is exactly how it looks like.