Given:
The equation is,
[tex]y=f(x)[/tex]
The point is,
[tex]P(-1,4)[/tex]
To find:
[tex]\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}[/tex]
Explanation:
i) The point is shifted 3 units up.
So, the point becomes,
[tex]P^{\prime}(-1,7)[/tex]
ii) The point is shifted 3 units left.
So, the point becomes,
[tex]P^{\prime}(-4,4)[/tex]
iii) Since it is stretched vertically by the scale factor of 3.
So, the point becomes,
[tex]P^{\prime}(-1,12)[/tex]
iv) Since it is compressed horizontally by the scale factor of 1/3.
So, the point becomes,
[tex]P^{\prime}(-\frac{1}{3},4)[/tex]
