Question

answer these questions please I'm really desperate. please im going to fail if I dont get this right

Answer 1

Answer-

$g(x)=-3x$

Solution-

First of all we have to get the value of f, as two point (0, -1) and (1, 2), we can get the equation by applying two point formula of straight line.

$\Rightarrow \dfrac{y-y_1}{y_2-y_1}=\dfrac{x-x_1}{x_2-x_1}$

$\Rightarrow \dfrac{y+1}{2+1}=\dfrac{x-0}{1-0}$

$\Rightarrow \dfrac{y+1}{3}=\dfrac{x}{1}$

$\Rightarrow \dfrac{y+1}{3}=x$

$\Rightarrow {y+1}=3x$

$\Rightarrow y=3x-1$

$\Rightarrow f(x)=3x-1$

Translating any point with coordinate as (x,y) 1 unit down, becomes (x, y-1)

So the new function will be,

$\Rightarrow (y-1)=3x-1$

$\Rightarrow y=3x$

Reflecting any point with coordinate as (x,y) over x axis, becomes (x, -y)

So the new function will be,

$\Rightarrow -y=3x$

$\Rightarrow y=-3x$

$\Rightarrow g(x)=-3x$