The function rule for function g is g(x) = 3³ˣ ⁻ ² + 4
The types of transformations that occur between function f and function g are horizontal scaling by a scale factor of ¹/₃ and followed by vertical translation by 4 units upwards from graph f(x)

<h3>Further explanation</h3>
Function is a relation which each member of the domain is mapped onto exactly one member of the codomain.
There are many types of functions in mathematics such as :
- <em>Linear Function → f(x) = ax + b</em>
- <em>Quadratic Function → f(x) = ax² + bx + c</em>
- <em>Trigonometric Function → f(x) = sin x or f(x) = cos x or f(x) = tan x</em>
- <em>Logarithmic function → f(x) = ln x</em>
- <em>Polynomial function → f(x) = axⁿ + bxⁿ⁻¹ + ...</em>

If function f : x → y , then inverse function f⁻¹ : y → x
Let us now tackle the problem!

<u>Given:</u>


<u>Asked:</u>
g(x) = ?
<u>Solution:</u>
If
, then:
→ Horizontal Scaling by a scale factor of ¹/₃ (Scaling in the x - direction) from graph f(x)


→ Vertical Translation by 4 units upwards (Translation in the y-direction) from graph h(x)


<h3>Conclusion:</h3>
The function rule for function g is 
The types of transformations that occur between function f and function g are horizontal scaling by a scale factor of ¹/₃ and followed by vertical translation by 4 units upwards from graph f(x)

<h3>Learn more</h3>
<h3>Answer details</h3>
Grade: High School
Subject: Mathematics
Chapter: Function
Keywords: Function , Trigonometric , Linear , Quadratic, Transformations
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