Functions and Relations Quiz

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Questions and Answers

Is the set of points {(5,3), (-2, 3), (6, 4), (1,1)} a function?

  • No, because 3 is repeated in the y-values.
  • Yes, because all x-values are unique. (correct)
  • No, because there is a point with duplicate coordinates.
  • Yes, because it passes the vertical line test.

What is the domain of the points {(3,-4), (2, 9), (3, -1), (1,5)}?

  • {3, 2, 1, -4}
  • {1, 2, 3, 4}
  • {3, 2, 1}
  • {1, 2, 3} (correct)

What is the range of the given set of points {(5,3), (-2, 3), (6, 4), (1,1)}?

  • {3, 4, 1}
  • {0, 1, 3, 4}
  • {1, 3, 4} (correct)
  • {1, 3}

Does the graph of a circle centered at the origin represent a function?

<p>No, it does not represent a function due to failing the vertical line test. (B)</p> Signup and view all the answers

What are the intercepts of a straight line graph?

<p>They are points where the line crosses the x-axis and y-axis. (C)</p> Signup and view all the answers

Evaluate f(6) for the function f(x) = 5x - 20.

<p>f(6) = 10.</p> Signup and view all the answers

Calculate g(-3) for g(x) = x² + 5x - 11.

<p>g(-3) = -17</p> Signup and view all the answers

What is the value of h(-8) if h(x) = |2x + 7|?

<p>h(-8) = 9.</p> Signup and view all the answers

Find the value of f(-1) + g(2) using f(x) = 3x - 5 and g(x) = 5 - x².

<p>f(-1) + g(2) = -8.</p> Signup and view all the answers

Determine f(x) when f(x) = 6.

<p>f(x) = 6 when x = 4.</p> Signup and view all the answers

Flashcards

Is {(5,3), (-2, 3), (6, 4), (1,1)} a function?

A relation is a function if each input (x-value) corresponds to exactly one output (y-value).

Domain of {(5,3), (-2, 3), (6, 4), (1,1)}

The set of all possible input values (x-coordinates).

Range of {(5,3), (-2, 3), (6, 4), (1,1)}

The set of all possible output values (y-coordinates).

Is a circle a function?

A circle is not a function because a single x-value can correspond to multiple y-values (vertically overlapping).

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Is a straight line a function?

A straight line is a function because each x-value corresponds to only one y-value (passes the vertical line test).

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f(6)

Substitute the value 6 for x in the function f(x) = 5x - 20 and then simplify. f(6) = (5 * 6) - 20

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g(-3)

Substitute the value -3 for x in the function g(x) = x² + 5x - 11 and then simplify. g(-3) = (-3)² + (5 * -3) - 11

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h(-8)

Substitute the value -8 for x in the function h(x) = |2x + 7| and then simplify. h(-8) = |(2 * -8) + 7|

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Evaluate f(-1) + g(2)

First, evaluate f(-1) by substituting -1 for x in the function f(x) = 5x - 20. Then, evaluate g(2) by substituting 2 for x in the function g(x) = x² + 5x - 11. Finally, add both results together.

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Solve for x when f(x) = 6

Set the function f(x) = 5x - 20 equal to 6 and solve for x. 5x - 20 = 6. Solve for x using algebra.

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Study Notes

Problem 7

  • The set of ordered pairs is {(5,3), (-2, 3), (6, 4), (1,1)}
  • Is this a function? Yes, each input has only one output.
  • What is the domain? {5, -2, 6, 1}
  • What is the range? {3, 4, 1}
  • What are the intercepts? None

Problem 8

  • The set of ordered pairs is {(3,-4), (2, 9), (3, -1), (1,5)}
  • Is this a function? No, the input 3 has two outputs (-4 and -1).
  • What is the domain? {3, 2, 1}
  • What is the range? {-4, 9, -1, 5}
  • What are the intercepts? None

Problem 9

  • Is this a function? No, it is a circle and hence fails the vertical line test.
  • What is the domain? All real numbers from -5 to +5
  • What is the range? All real numbers from -5 to +5
  • What are the intercepts? (0, 0)

Problem 10

  • Is this a function? Yes, the graph passes the vertical line test.
  • What is the domain? All real numbers
  • What is the range? All real numbers greater than or equal to -2
  • What are the intercepts? (0, -1)

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