Question

For the function defined by... Precalculus question?

Answer 1

For the function defined by: f(x) = \[f(x) = \left[\begin{matrix}x^2 & x \le 1 \\ 2x+1 & x<1\end{matrix}\right] \]

Answer 2

Pretend the brackets look like these { }

Answer 3

Part 1: Evaluate f(0).

Part 2: Graph f(x).

Answer 4

can you check your function again and make sure the inequalities are posted correctly?

Answer 5

there is some ambiguity in the question
because f(0)=0 by the first equation.
also f(0)=2*0+1=1 by the second eq.

Answer 6

Oops - the last inequality (bottom right) should be x>1

Answer 7

ok cool

Answer 8

Also note that the brackets on the end are actually squiggly lines { }

Answer 9

so, if x = 0, which function do we use?

Answer 10

Do you know how to do it?

Answer 11

yes

Answer 12

f(0) means evaluate the function when x = 0

now, this function has two rows. one row is when x >= 1 and the other row is when x < 1

Answer 13

f=0 would make all equations true except the bottom left one.. is that what you're asking?

Answer 14

yes, since x = 0 we only use the top row

Answer 15

so, if f(x) = x^2, when x = 0, what is f(x)?

Answer 16

I'm just not sure how to do it since there are four different functions... is it a matrix?

Answer 17

there are only two functions

Answer 18

good, so f(0) = 0

Answer 19

this is how the function works

Answer 20

It would equal 0

Answer 21

this means that f(x) = x^2 when x <=1

Answer 22

the second row means that

f(x) = 2x + 1 when x > 1

make sense?

Answer 23

Hold on, let me look at this

Answer 24

Not quite sure what you mean

Answer 25

Why are we only using the top two equations?

Answer 26

there are two equations

Answer 27

the x <=1 part is not an equation, it tells us to use x^2 only when x <=1

Answer 28

since 0 is less than 1, we use x^2

Answer 29

make sense?

Answer 30

Oh I see

Answer 31

so, for the graphing part:

Answer 32

That clears things up!

Answer 33

for graphing, all you do is graph

x^2 but only for x <=1

Answer 34

so your graph will look like this

Answer 35

So we would use the first one because x is less than or equal to 1?

Answer 36

yes

Answer 37

Ah okay

Answer 38

Thanks so much for your help! I think I got it from here