Question

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?

Answer 1

Answer:

f(x)=2(x-3)-2

Step-by-step explanation:

when you hear if it translate to the right, it mean subtract " - "

so translate 3 unit right, it mean minus 3.

and same if translate left, it mean add, "+"

But if it mean shift down, it mean minus -

and if it mean shift up, it mean add +

so shift down 2 unit, mean -2

stretch factor of 2, mean multiply by 2

I hope this help! Im gonna explain further more if you have any question☺

Answer 2

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

The new function is: $f"(x) = 2(x- 1)^2 - 14$

The function is given as:

$f(x) = (x + 2)^2 - 5$

When translated right, the rule is:

$(x,y) \to (x - h, y)$

In this case;

$h= 3$ --- i.e. 3 units right

So, the function becomes

$f'(x) = (x + 2 - 3)^2 - 5$

$f'(x) = (x - 1)^2 - 5$

When shifted down, the rule is:

$(x,y) \to (x, y - b)$

In this case;

$b =2$  --- i.e. 2 units down

So, the function becomes

$f'(x) = (x- 1)^2 - 5-2$

$f'(x) = (x- 1)^2 - 7$

When vertically stretched, the rule is:

$(x,y) \to (x, ay)$

In this case;

$a =2$  --- i.e. factor of 2

So, the function becomes

$f"(x) = 2*[(x- 1)^2 - 7]$

$f"(x) = 2(x- 1)^2 - 14$

Hence, the new function is: $f"(x) = 2(x- 1)^2 - 14$

Read more about function transformations at:

brainly.com/question/24326503