Question

Drag Each tile to the correct location. Not all tiles will be used. Match The transformation of rational function f(x)=2x/x-3 with the resulting function each tile to the correct location.

Answer 1

See explanation below

Step-by-step explanation:
`f(x)\text{ = }\frac{2x}{x\text{ - 3}}`

For the first function in the box:

`\begin{gathered} f(x)\text{ = }\frac{2x}{x\text{ - 3}}+\text{ 5} \\ 5\text{ units was added to the y coordinates. \% is positive meaning translation would be up} \\ \text{This means there is a translation of 5 units up} \end{gathered}`

For the 2nd function (right) in the box:

`\begin{gathered} f(x)\text{ = }\frac{-2x}{-x\text{ - 3}} \\ \text{From the above: } \\ \text{when we compared with th original fucntion, we would s}ee\text{ the x coordinate is negated} \\ \text{This is a reflection over the y ax is. In thos reflection, the y ax i}s\text{ remains the same.} \\ \text{While the x ax i}s\text{ is negated.} \end{gathered}`

The answer is a reflection across the y - axis

For the 3rd function (bottom) in the box:

`\begin{gathered} f(x)\text{ = }\frac{10x}{x\text{ - 3}}\text{= 5(}\frac{2x}{x\text{ - 3}}) \\ \text{Comparing, we would see 5 was multiplied to the y ax i}s \\ A\text{ multiplication that is positive is a vertical stretch} \\ \text{This is a vertical stretch by 5} \end{gathered}`

For the 4th function (bottom) in the box:

`\begin{gathered} f(x)\text{ = }\frac{2(x\text{ + 5)}}{(x\text{ + 5)}-3} \\ A\text{ function translation to the right = f(x - h)} \\ \text{But we have }(x\text{ + 5) = (x - (-5)); h = -5} \\ In\text{ this function, the x is translated 5 units to the left} \end{gathered}`