Can someone explain this to me? (1 Viewer)

RakeshCristoval · Feb 16, 2021

Have my first ever econ1202 lecture and just do not understand what my lecturer is doing with the examples ( f(x) =2, f(x) = 1 + 0.5x and so on ) he is giving in the pic below. Was wondering if someone could explain what is going on here lol. Cheers

Qeru · Feb 16, 2021

RakeshCristoval said:
Have my first ever econ1202 lecture and just do not understand what my lecturer is doing with the examples ( f(x) =2, f(x) = 1 + 0.5x and so on ) he is giving in the pic below. Was wondering if someone could explain what is going on here lol. Cheers

The general form of a polynomial is: $f(x)=c_nx^n+c_{n-1}x^{n-1}+...+c_1x+c_0$

where all the c's are constants and all the x's are variables

ANY polynomial can be represented in this form. For example if I let $c_1=0.5$ and $c_0=1$ and every other c=0 notice how the only terms im left with are the $c_1$ and $c_0$ terms (all the other terms become zero) so the polynomial becomes: $f(x)=0.5x+1$ . This is just one specific random example of a polynomial.

RakeshCristoval · Feb 16, 2021

Qeru said:
The general form of a polynomial is: $f(x)=c_nx^n+c_{n-1}x^{n-1}+...+c_1x+c_0$

where all the c's are constants and all the x's are variables

ANY polynomial can be represented in this form. For example if I let $c_1=0.5$ and $c_0=1$ and every other c=0 notice how the only terms im left with are the $c_1$ and $c_0$ terms (all the other terms become zero) so the polynomial becomes: $f(x)=0.5x+1$ . This is just one specific random example of a polynomial.

I sort of get that but in the third example, why is c2=1? Where is he getting that?

Qeru · Feb 16, 2021

RakeshCristoval said:
I sort of get that but in the third example, why is c2=1? Where is he getting that?

$c_0$ corresponds to the constant term, $c_1$ corresponds to to the term in x. $c_2$ corresponds to the term in $x^2$ c_3 corresponds to the term in $x^3$ and so on. So by letting $c_2=1$ your letting the coefficient of $x^2$ equal to 1, and all the other c's are zero so they all cancel.

RakeshCristoval · Feb 16, 2021

Qeru said:
$c_0$ corresponds to the constant term, $c_1$ corresponds to to the term in x. $c_2$ corresponds to the term in $x^2$ c_3 corresponds to the term in $x^3$ and so on. So by letting $c_2=1$ your letting the coefficient of $x^2$ equal to 1, and all the other c's are zero so they all cancel.

this makes much more sense thank you!

Can someone explain this to me? (1 Viewer)

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