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((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*3,2),(0*3,1),(4*3,5)\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*-1),(0,1*-1),(12,5*-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`