Answer :

For the following function, we have that:

  • The domain is 0 < x ≤ 4.
  • The range is -2 ≤ y ≤ 2.
  • The x-intercepts are x = 1 and x = 3, that is, points (1,0) and (3,0).
  • The y-intercept is y = 2, that is, point (0,2).
  • The maximum value on the interval [1,4] is of 2, at point (4,2).
  • The minimum value on the interval [1,4] is of -2, at point (2,-2).

What are the domain and the range of a function?

  • The domain of a function is the set that contains all the values of the input.
  • The range of a function is the set that contains all the values of the output.

In a graph:

  • The domain is given by the x-values, the horizontal axis.
  • The range is given by the y-values, the vertical axis.

Hence, for the graph in this problem, we have that:

  • The domain is 0 < x ≤ 4.
  • The range is -2 ≤ y ≤ 2.

What are the intercepts of a function?

  • The x-intercept of a function is given by the value of x when f(x) = 0, that is, the value of x when the function crosses the x-axis.
  • The y-intercept of a function is given by the value of f(x) when x = 0, that is, the value of y when the function crosses the y-axis.

Hence:

  • The x-intercepts are x = 1 and x = 3, that is, points (1,0) and (3,0).
  • The y-intercept is y = 2, that is, point (0,2).

What is the maximum and the minimum value?

We have to look at the values of y on the interval, hence:

  • The maximum value on the interval [1,4] is of 2, at point (4,2).
  • The minimum value on the interval [1,4] is of -2, at point (2,-2).

More can be learned about functions at https://brainly.com/question/24808124

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