Firstly, we are given the points.
[tex]\left\lbrace (-3,2),(0,1),(4,5)\right\rbrace [/tex]The points are taken from a function f.
Let's assume the function is;
[tex]y=f(x)[/tex]The coordinates of these three points are taken through horizontal stretch by a factor of 3.
For an horizontal stretch of a factor of 3, the function becomes;
[tex]y=f(\frac{x}{3})[/tex]So, to attain the same value of y, x values need to be trippled.
That means all x coordinates would be multiplied by 3.
So, we then have the coordinates;
[tex]\begin{gathered} \left\lbrace (-3\times3,2),(0\times3,1),(4\times3,5)\right\rbrace \\ \left\lbrace (-9,2),(0,1),(12,5)\right\rbrace \end{gathered}[/tex]Then it was followed by a reflection across the x-axis.
For reflection across the x-axis, the y coordinates would be multiplied by -1.
[tex](x,y)\rightarrow(x,-y)[/tex]The coordinates will then become;
[tex]\begin{gathered} \left\lbrace (-9,2\times-1),(0,1\times-1),(12,5\times-1)\right\rbrace \\ \left\lbrace (-9,-2),(0,-1),(12,-5)\right\rbrace \end{gathered}[/tex]So, the coordinates of these three points after a horizontal stretch by a factor of 3, followed by a reflection across the x-axis is;
[tex]\left\lbrace (-9,-2),(0,-1),(12,-5)\right\rbrace [/tex]