Question

The points {(-3, 2), (0, 1), (4,5)} are on the graph of function f. What are the coordinates of these threepoints after a horizontal stretch by a factor of 3, followed by a reflection across the x-axis?© {-1.-2.6.-».(3-4

Answer 1

Firstly, we are given the points.

$\left\lbrace (-3,2),(0,1),(4,5)\right\rbrace$

The points are taken from a function f.

Let's assume the function is;

$y=f(x)$

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;

$y=f(\frac{x}{3})$

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;

$\begin{gathered} \left\lbrace (-3\times3,2),(0\times3,1),(4\times3,5)\right\rbrace \\ \left\lbrace (-9,2),(0,1),(12,5)\right\rbrace \end{gathered}$

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.

$(x,y)\rightarrow(x,-y)$

The coordinates will then become;

$\begin{gathered} \left\lbrace (-9,2\times-1),(0,1\times-1),(12,5\times-1)\right\rbrace \\ \left\lbrace (-9,-2),(0,-1),(12,-5)\right\rbrace \end{gathered}$

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;

$\left\lbrace (-9,-2),(0,-1),(12,-5)\right\rbrace$