Answered

Find the best solutions to your problems with the help of IDNLearn.com's experts. Explore a wide array of topics and find reliable answers from our experienced community members.

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
Thank you for using this platform to share and learn. Keep asking and answering. We appreciate every contribution you make. Thank you for trusting IDNLearn.com. We’re dedicated to providing accurate answers, so visit us again for more solutions.