Web Analytics

Verified Answer :

Answer:

g(x) = 3x² + 8

Step-by-step explanation:

Let f(x) = 3x² + 5

Now, the given function f(x) is translated up by 3 units and is equal to g(x)

And according to the rule of translation , if the graph of a function f(x) is to be translated up by c units then the equation becomes f(x) + c

Since, the graph is translated by 3 units

⇒ g(x) = f(x) + 3

⇒ g(x) = 3x² + 5 + 3

⇒ g(x) = 3x² + 8

facundo3141592

Translating the function 3 units up, we will get g(x) = 3x^2 + 8

How do translations work?

There are two general types of translations.

Horizontal translation:

For a general function f(x), a horizontal translation of N units is written as:

g(x) = f(x + N).

  • If N is positive, the shift is to the left.
  • If N is negative, the shift is to the right.

Vertical translation:

For a general function f(x), a vertical translation of N units is written as:

g(x) = f(x) + N.

  • If N is positive, the shift is upwards.
  • If N is negative, the shift is downwards.

Here we start with the function:

f(x) = 3x^2 + 5

And then we translate it up 3 units, then the function g(x) will be:

g(x) = 3x^2 + 5 + 3

g(x) = 3x^2 + 8

If you want to learn more about transformations, you can read:

https://brainly.com/question/3333365

Related Questions