Question

given f(x)=3^x-2 and g(x)=f(3x)+4, write the function rule for function g and describe the types of transformations that occur between function f and function g

Answer 1

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)

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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 + ...

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If function f : x → y , then inverse function f⁻¹ : y → x

Let us now tackle the problem!

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Given:

$f(x) = 3^{x - 2}$

$g(x) = f(3x) + 4$

Asked:

g(x) = ?

Solution:

If $f(x) = 3^{x - 2}$ , then:

$h(x) = f(3x)$ → Horizontal Scaling by a scale factor of ¹/₃ (Scaling in the x - direction) from graph f(x)

$h(x) = 3^{3x - 2}$

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

$g(x) = 3^{3x - 2} + 4$

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Conclusion:

The function rule for function g is $\boxed{ g(x) = 3^{3x - 2} + 4 }$

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)

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Learn more

• Inverse of Function : brainly.com/question/9289171
• Rate of Change : brainly.com/question/11919986
• Graph of Function : brainly.com/question/7829758

Answer details

Grade: High School

Subject: Mathematics

Chapter: Function

Keywords: Function , Trigonometric , Linear , Quadratic, Transformations

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Answer 2

Answer:

g(x) = 3^(3x-2)+ 4

transformations: horizontal compression and vertical translation

Step-by-step explanation:

Given

f(x)=3^(x-2)

To get f(3x) replace x by 3x:

f(3x) = 3^[(3x)-2] = 3^(3x-2)  

Add 4 to that result and get g(x):

g(x)=f(3x)+4 = 3^(3x-2)+ 4

g(x) has two parts, 'f(3x)' and '+ 4'

f(3x) -> horizontal compression by a factor of 3

+ 4 -> vertical translation up 4 units