Key Features of Functions Practice

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Questions and Answers

What is the domain of the function in graph 1?

  • (-8, 4)
  • (-∞, -8) U (4, ∞)
  • (-40, 40) (correct)
  • (-∞, -40) U (40, ∞)

What is the range of the function in graph 2?

  • (-2, 8)
  • (2, 8) (correct)
  • (-∞, ∞)
  • (-∞, 2) U (4, ∞)

What is the x-intercept of the function in graph 1?

  • -20
  • 0
  • 4
  • -8 (correct)

What is the y-intercept of the function in graph 2?

<p>2 (B)</p> Signup and view all the answers

Over which interval is the function in graph 1 increasing?

<p>no interval (A)</p> Signup and view all the answers

What is the average rate of change of the function in graph 1 over the interval [-5, 0]?

<p>-20/5 (A)</p> Signup and view all the answers

What is the interval where the function in graph 1 is positive?

<p>(-20, 40) (D)</p> Signup and view all the answers

What is the interval where the function in graph 2 is decreasing?

<p>(-2, 0) (C)</p> Signup and view all the answers

Flashcards

Domain of a function

All possible input values (x-values) for which a function is defined.

Range of a function

All possible output values (y-values) that a function can produce.

X-intercept

The point(s) where a function intersects the x-axis, having a y-value of zero.

Y-intercept

The point(s) where a function intersects the y-axis, having an x-value of zero.

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Increasing interval

An interval on the x-axis where the y-values of the function are increasing as x increases.

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Average rate of change

The ratio of the change in y-values to the change in x-values over a given interval.

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Positive interval

The interval(s) on the x-axis where the y-values of the function are greater than zero.

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Decreasing interval

An interval on the x-axis where the y-values of the function are decreasing as x increases.

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Study Notes

Key Features of Functions

  • Function 1 has a domain of x = 40 and a range of y = 20.
  • The x-intercepts of function 1 are at x = -8, -4, 0, 4, and 8.
  • The y-intercept of function 1 is at y = -20.
  • Function 1 is positive on the interval -40 and negative on the interval not specified.
  • The function is increasing on the interval not specified and decreasing on the interval not specified.
  • The average rate of change of function 1 over the interval [-5, 0] is not specified.

Second Function

  • Function 2 has a domain of x = 8 and a range of y not specified.
  • The x-intercepts of function 2 are at x = 4.
  • The y-intercept of function 2 is at y = 2.
  • Function 2 is positive on the interval x and negative on the interval not specified.
  • The function is increasing on the interval not specified and decreasing on the interval not specified.
  • The average rate of change of function 2 over the interval [-2, 0] is not specified.

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