Question

(i) y = f(x) + 3(ii) y = f (x + 3)(iii) y = 3f(x)(iv) y = f(3x)

Answer 1

Given:

The equation is,

`y=f(x)`

The point is,

`P(-1,4)`

To find:

`\begin{gathered} \left(i\right)y=f(x)+3 \\ (ii)y=f(x+3) \\ \left(iii\right)y=3f\mleft(x\mright) \\ \left(iv\right)y=f(3x) \end{gathered}`

Step-by-step explanation:

i) The point is shifted 3 units up.

So, the point becomes,

`P^(\prime)(-1,7)`

ii) The point is shifted 3 units left.

So, the point becomes,

`P^(\prime)(-4,4)`

iii) Since it is stretched vertically by the scale factor of 3.

So, the point becomes,

`P^(\prime)(-1,12)`

iv) Since it is compressed horizontally by the scale factor of 1/3.

So, the point becomes,

`P^(\prime)(-(1)/(3),4)`