Question

For the function defined by: \[f(x) = \left[\begin{matrix}x^2 & x \le1 \\ 2x+1 & x>1\end{matrix}\right]\] evaluate f(0) and identify the function that will be used when x=0.

Answer 1

Try using `\begin{cases}...\end{cases}`

Answer 2

would f(0) be \[\left[\begin{matrix}0 & 0\le1 \\ 1 & 0\ge1\end{matrix}\right]\] ?

Answer 3

no \(f(0)\) is one number

Answer 4

is \(0\le 1\) or is \(0>1\) true?

Answer 5

so what do i do if it says to evaluate f(0)?

Answer 6

Since the top one's condition is true, it's expression represents \(f(0)\)

Answer 7

answer my question above, then we will know

Answer 8

@satellite73 i dont know exactly what you mean, but its in matrix form and told me to evaluate it by f(0)

Answer 9

\[f(x) = \left\{\begin{array}{rcc}
x^2 & \text{if} & x \leq 0 \\
2x+1& \text{if} & x>0
\end{array}
\right.
\]

Answer 10

this is what the question is!

Answer 11

they omitted the word "if"
which means, if the input is less than or equal to zero, use the top formula
for example \[f(-5)=(-5)^2=25\] since \(-5<0\)

Answer 12

whereas if the input is larger than zero, use the bottom formula
for example
\[f(10)=2\times 10+1=21\] since \(10>0\)

Answer 13

since \(0\) is less than one, use the top formula

Answer 14

i.e. use \(f(0)=0^2=0\)

Answer 15

f(0) = 0^2=0, 0<=1, 2(0)+1=1, 0>1 would be the answer?

Answer 16

no no the answer is one number

Answer 17

the stuff to the right tells you what equation to use depending on what number you have

Answer 18

so would the answer be just 0?

Answer 19

yes, just zero

Answer 20

i think you are confused by what this means
it is called a piecewise function
it is defined in different ways depending on the value of the input

Answer 21

so what does it mean when it says to identify the function that will be used when x = 0?

Answer 22

it means out of the two formulas \(x^2\) or \(2x+1\) which would you use

Answer 23

since \(0<1\) you use the top one \(x^2\) and not the bottom one \(2x+1\)

Answer 24

but if you wanted \(f(5)\) you would use the bottom one since \(5>1\)

Answer 25

i.e. \(f(5)=2\times 5+1=11\)
you wouldn't square it, since 5 is larger than 1

Answer 26

i just dont understand where you're getting the numbers from and i dont know how to get the answers that i need D:

Answer 27

i am making them up

Answer 28

you need to learn how to read this to do the problem
the stuff on the right tells you which formula to use

Answer 29

lets just answer the quesion
A) you would use the top expression \(x^2\) since \(0<1\)
B) \(f(0)=0^2=0\)

Answer 30

so if i use x^2, i get 0

Answer 31

yes

Answer 32

okay, how do i find the others now? :o

Answer 33

what others?

Answer 34

so to answer the question "identify the function that will be used when x=0" it would just be 0?

Answer 35

because i have 2 questions. 1 that says "identify the function that will be used when x=0" & "find the value of this function when x=0" so what would the difference between the two answers be?

Answer 36

i wrote the answers above exactly as A and B

Answer 37

oh i see! im so sorry, thanks!!! :)

Answer 38

now part II is saying "Graph f(x). Graph the first function completely."

Answer 39

i know it is now f(0) but how do i graph this? @satellite73