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1: Write a function that represents this process:
Take a number, x.
Multiply it by 4.
Subtract 2 from the result.
Then find the inverse of this function. Does the inverse represent the reverse of the process above? Explain why or why not.
2:Show why, for linear functions, a vertical translation is equivalent to a horizontal translation. For a linear function, what horizontal translation is equivalent to a vertical translation of 3 units up?
3:Alex says that the function f(x) = (3x)2 represents a vertical stretch of the quadratic parent function by a factor of 3. Marta says that it represents a horizontal compression by a factor of . Decide whether one student is correct, both are correct, or neither is correct.
4:For an unknown parent function f(x), write a function g(x) that is:
vertically stretched by a factor of 2,
shifted up 5 units, and
shifted right 4 units.
Explain how your function accomplishes these transformations.

Sagot :

snehashish65

Original function involved multiplication by 4 and then subtraction of 2.

Inverse function involves addition of 2 and then division by 4.

So the inverse represents the reverse of the given process.

What is function?

A function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.

According to the function,

Let the function be represented by f(x).

Step 1- Multiplying the number x by 4 results in 4x.

Step 2 - Subtracting 2 from results give 4x - 2.

So the function becomes:

f(x) = 4x - 2

We will find the inverse function by Replacing f(x) by y, and isolate x on one side of the equation and find the inverse:

[tex]y=4x-2\\\\ < br/ > y+2=4x\\ < br/ > x =\frac{1}{4} (y+2)\\ < br/ > f^-^1(y) = \frac{1}{4} (y+2)\\ < br/ > f^-^1(x) = \frac{1}{4} (x+2)[/tex]

Here,

The inverse function represents the reverse process.

Here, Original function involved multiplication by 4 and then subtraction of 2.

Inverse function involves addition of 2 and then division by 4.

So the inverse represents the reverse of the given process.

Learn more about Function here:https://brainly.com/question/12431044

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