Answered

Discover the answers to your questions at Westonci.ca, where experts share their knowledge and insights with you. Get immediate answers to your questions from a wide network of experienced professionals on our Q&A platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.

the function f(x)= x1/3 is transformed to get function h. h(x)= (2x)1/3+5 which statements are true about function h

Sagot :

The transformation of a function may involve any change. The function f(x) is vertically stretched and shifted 5 units upwards to form h(x).

How does the transformation of a function happen?

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs) etc.

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

  • Left shift by c units, y=f(x+c) (same output, but c units earlier)
  • Right shift by c units, y=f(x-c)(same output, but c units late)

Vertical shift

  • Up by d units: y = f(x) + d
  • Down by d units: y = f(x) - d

Stretching:

  • Vertical stretch by a factor k: y = k \times f(x)
  • Horizontal stretch by a factor k: y = f(\dfrac{x}{k})

The function f(x)=x^(1/3) is transformed to form the function of  h(x)=(2x)^(1/3)+5. Therefore, the transformation made to the function is,

Vertically stretched by a factor of 2^(1/3) ⇒ 2^(1/3) × x^(1/3) = (2x)^(1/3)

Up by 5 units ⇒ (2x)^(1/3) + 5

Hence, the function f(x) is vertically stretched and shifted 5 units upwards to form h(x).

Learn more about Transforming functions:

https://brainly.com/question/17006186

#SPJ1

View image ap8997154
We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.