Question

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

Answer 1

`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 (y-y_1)/(y_2-y_1)=(x-x_1)/(x_2-x_1)`

`\Rightarrow (y+1)/(2+1)=(x-0)/(1-0)`

`\Rightarrow (y+1)/(3)=(x)/(1)`

`\Rightarrow (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`