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Tia states that the graph of g(x) = (x – 2)3 + 7 is a translation of 2 units to the left and 7 units up from f(x) = x 3. Is Tia’s description of the translations correct? Explain.

Respuesta :

luisejr77

Answer: No, Tia's description is not correct.

Step-by-step explanation:

Some transformations for a function f(x) are shown below:

If [tex]f(x)+k[/tex], the function is shifted up "k" units.

If [tex]f(x)-k[/tex], the function is shifted down "k" units.

If [tex]f(x+k)[/tex], the function is shifted left "k" units.

If [tex]f(x-k)[/tex], the function is shifted right "k" units.

Knowing this, and given the function g(x):

[tex]g(x)=(x-2)^3+7[/tex]

And the parent function:

[tex]f(x)=x^3[/tex]

 You can identify that the graph of the function g(x) is a translation of 2 units to the right and 7 units up from the parent function f(x).

Therefore, Tia's description is not correct.

johanrusli

Tia’s description of the translations is not correct

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 + ...

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

Let us now tackle the problem!

Given:

[tex]f(x) = x^3[/tex]

[tex]h(x) = ( x - 2 )^3[/tex] → Translation of 2 units to the right from graph f(x)

[tex]g(x) = ( x - 2 )^3 + 7[/tex] → Translation of 7 units up from graph h(x)

Therefore , Tia's description of the translations is not correct. Tia should state that the graph of g(x) = ( x - 2 )³ + 7 is a translation of 2 units to the right and 7 units up from f(x) = x³.

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

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