Discover answers to your questions with Westonci.ca, the leading Q&A platform that connects you with knowledgeable experts. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.

Please help so confused

Please Help So Confused class=

Sagot :

Answer:

  • turning point: (0, -1)
  • domain, range: all real numbers
  • x-intercept: (1/27, 0)
  • y-intercept: (0, -1)
  • transformations: vertical expansion by a factor of 3; translation down 1

Step-by-step explanation:

There are a couple of transformations that may be of interest:

  g(x) = k·f(x) . . . . vertical scaling by a factor of k

  g(x) = f(x) +k . . . vertical translation by k units (up)

  g(x) = f(x -k) . . . horizontal translation by k units (right); not used here

__

Unlike the square root function, which is undefined for negative values, the cube root function is defined for all real numbers. Its domain and range are all real numbers.

The turning point of a cube-root function is the origin. Here, that has been translated down 1 unit, so it is (0, -1). That is also the y-intercept.

The x-intercept is the value of x where g(x)=0:

  0 = 3∛x -1

  1 = 3∛x

  1/3 = ∛x

  (1/3)³ = x = 1/27

The x-intercept is (1/27, 0).

__

Transformations

As we discussed above, the addition of -1 to the parent function causes it to be translated down 1 unit.

The multiplication of the parent function by 3 causes it to be vertically expanded by a factor of 3.

View image sqdancefan