Question

Four transformations of the Function f(x)=2^x are given below.
For each transformation drag the expression that shows the result of that transformation to the box under it.

Answer 1

After applying operations between functions, we find the following four transformations for the function $f(x) = 2^{x}$:

a) 6 · f(x) - $g(x) = 6 \cdot 2^{x}$

b) f(6 · x) - $g(x) = 2^{6\cdot x}$/$g(x) = 2^{6}\cdot f(x)$

c) f(x + 6) - $g(x) = 2^{x+6}$/$g(x) = 2^{6}\cdot f(x)$

d) f(x) + 6 - $g(x) = 2^{x}+6$

How to determine the transformations of a function

Mathematically speaking, transformations are operations applied on a function such that its domain or range are altered. There are five operations for functions:

1. Addition
2. Subtraction
3. Multiplication
4. Division
5. Composition

Let suppose that $f(x) = 2^{x}$, the images of this function are, respectively:

a) 6 · f(x) - Multiplication between two functions

$g(x) = 6 \cdot 2^{x}$

b) f(6 · x) - Composition between two functions

$g(x) = 2^{6\cdot x}$

$g(x) = (2^{x})^{6}$

$g(x) = (f(x))^{6}$

c) f(x + 6) - Composition between two functions

$g(x) = 2^{x+6}$

$g(x) = 2^{x}\cdot 2^{6}$

$g(x) = 2^{6}\cdot 2^{x}$

$g(x) = 2^{6}\cdot f(x)$

d) f(x) + 6 - Addition between two functions

$g(x) = 2^{x}+6$

To learn more on transformations: https://brainly.com/question/23277077

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