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)
[tex]\texttt{ }[/tex]
Further explanation
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 :
- Linear Function → f(x) = ax + b
- Quadratic Function → f(x) = ax² + bx + c
- Trigonometric Function → f(x) = sin x or f(x) = cos x or f(x) = tan x
- Logarithmic function → f(x) = ln x
- Polynomial function → f(x) = axⁿ + bxⁿ⁻¹ + ...
[tex]\texttt{ }[/tex]
If function f : x → y , then inverse function f⁻¹ : y → x
Let us now tackle the problem!
[tex]\texttt{ }[/tex]
Given:
[tex]f(x) = 3^{x - 2}[/tex]
[tex]g(x) = f(3x) + 4[/tex]
Asked:
g(x) = ?
Solution:
If [tex]f(x) = 3^{x - 2}[/tex] , then:
[tex]h(x) = f(3x)[/tex] → Horizontal Scaling by a scale factor of ¹/₃ (Scaling in the x - direction) from graph f(x)
[tex]h(x) = 3^{3x - 2}[/tex]
[tex]\texttt{ }[/tex]
[tex]g(x) = h(x) + 4[/tex] → Vertical Translation by 4 units upwards (Translation in the y-direction) from graph h(x)
[tex]g(x) = 3^{3x - 2} + 4[/tex]
[tex]\texttt{ }[/tex]
Conclusion:
The function rule for function g is [tex]\boxed{ g(x) = 3^{3x - 2} + 4 }[/tex]
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)
[tex]\texttt{ }[/tex]
Learn more
- Inverse of Function : https://brainly.com/question/9289171
- Rate of Change : https://brainly.com/question/11919986
- Graph of Function : https://brainly.com/question/7829758
Answer details
Grade: High School
Subject: Mathematics
Chapter: Function
Keywords: Function , Trigonometric , Linear , Quadratic, Transformations
#LearnWithBrainly
