A student graphed function f(x) =( x+2)² - 5. How would the new function be written if it is translated 3 units to the right, shifted 2 units down and vertically stretched by a factor of 2?

The transformation of a function involves changing the features of the original function to another.

The new function is:

The function is given as:

When translated right, the rule is:

In this case;

--- i.e. 3 units right

So, the function becomes

When shifted down, the rule is:

In this case;

 --- i.e. 2 units down

So, the function becomes

When vertically stretched, the rule is:

In this case;

 --- i.e. factor of 2

So, the function becomes

Hence, the new function is:

Read more about function transformations at:

step-by-step explanation:

you can add the two numbers and divide the result by 2. or you can find the gap between the two numbers and add half of this to the smaller number.