Question

Which two transformations can be used to

Answer 1

We have been given that that function $y=3(x-5)^2$ is obtained from the graph of $y=x^2$. We are asked to find the two transformations that can be used to obtain the transformed function.

We will use transformation rules to solve our given problem.

$f(x-a)\Rightarrow\text{Graph shifted to the right by a units}$, where a is any positive number.

We can see that the value of a is 5 for our given function, therefore, graph is shifted to right by 5 units.

Now we will use scaling rules.

$f(x)\Rightarrow a\cdot f(x)$

If $a>1$, then function is stretched vertically by a factor of 'a'.

If $a$, then function is compressed vertically by a factor of 'a'.

We can see that value of a is 3. Since 3 is greater than, so function will be stretched vertically by a factor of 3.

Therefore, the function can be obtained by a vertical stretch and translation of 5 units to right and option J is the correct choice.