Function Evaluation and Representation Quiz

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Questions and Answers

If f(x) = 3x + 2, find f(4)

14

If f(x) = 3x + 2, find f(8)

26

If f(x) = 3x + 2, find f(-2)

-4

If f(x) = 3x + 2, find f(1) - 1

<p>4</p> Signup and view all the answers

If f(x) = 3x + 2, find f(2) + 1

<p>9</p> Signup and view all the answers

If f(x) = 3x + 2, find f(x + 1)

<p>3x + 5</p> Signup and view all the answers

If g(x) = x² - x, find g(2)

<p>2</p> Signup and view all the answers

If g(x) = x² - x, find g(-3)

<p>12</p> Signup and view all the answers

If g(x) = x² - x, find g(-6)

<p>42</p> Signup and view all the answers

If g(x) = x² - x, find g(2) - 2

<p>0</p> Signup and view all the answers

If g(x) = x² - x, find g(-1) + 4

<p>6</p> Signup and view all the answers

If g(x) = x² - x, find g(3b)

<p>9b² - 3b</p> Signup and view all the answers

If f(x) = 2x², find f(3)

<p>18</p> Signup and view all the answers

If f(x) = 2x², find f(-4)

<p>32</p> Signup and view all the answers

If f(x) = 2x², find f(5) + 1

<p>51</p> Signup and view all the answers

If f(x) = 2x², find f(-6) - 5

<p>67</p> Signup and view all the answers

If g(x) = 3x² + 2x - 1, find g(0)

<p>-1</p> Signup and view all the answers

If g(x) = 3x² + 2x - 1, find g(2)

<p>15</p> Signup and view all the answers

If g(x) = 3x² + 2x - 1, find g(-3)

<p>20</p> Signup and view all the answers

If g(x) = 3x² + 2x - 1, find g(-3) + 2

<p>22</p> Signup and view all the answers

Does this represent a function: {(2, 5), (4, -2), (3, 3), (5, 4), (-2, 5)}?

<p>True (A)</p> Signup and view all the answers

Does this represent a function: {(6, -1), (-4, 2), (5, 2), (4, 6), (6, 5)}?

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

Does this represent a function: y = x + 3?

<p>True (A)</p> Signup and view all the answers

Does this represent a function: x = 2?

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

Does this represent a function: y = 1?

<p>True (A)</p> Signup and view all the answers

Does this represent a function: y = -3?

<p>True (A)</p> Signup and view all the answers

Does this represent a function: a horizontal line?

<p>True (A)</p> Signup and view all the answers

Does this represent a function: a vertical line?

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

Does this represent a function: a table with a repeated x-value?

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

Does this represent a function: a table with no repeating x-values?

<p>True (A)</p> Signup and view all the answers

What is the domain?

<p>the list of x-values</p> Signup and view all the answers

What is the range?

<p>the list of y-values</p> Signup and view all the answers

Find the domain for: {(4, 3), (-1, 4), (3, -2), (-2, 1)}

<p>{4, -1, 3, -2}</p> Signup and view all the answers

Find the range for: {(4, 3), (-1, 4), (3, -2), (-2, 1)}

<p>{3, 4, -2, 1}</p> Signup and view all the answers

Find the domain for: {(0, 9), (0, 8), (1, 2), (4, 3)}

<p>{0, 1, 4}</p> Signup and view all the answers

Find the range for: {(0, 9), (0, 8), (1, 2), (4, 3)}

<p>{9, 8, 2, 3}</p> Signup and view all the answers

Find the domain for: {(3, 1), (2, 3), (3, 2), (2, 1)}

<p>{3, 2}</p> Signup and view all the answers

Find the range for: {(3, 1), (2, 3), (3, 2), (2, 1)}

<p>{1, 3, 2}</p> Signup and view all the answers

What are independent variables?

<p>the domain is the list of</p> Signup and view all the answers

What are dependent variables?

<p>the range is the list of</p> Signup and view all the answers

Is 3x + 2y = 9 linear or nonlinear?

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

Is 5x = 10 linear or nonlinear?

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

Is 3x = 2 linear or nonlinear?

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

Is 2y = -4 linear or nonlinear?

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

Is -5y = 20 linear or nonlinear?

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

Is 7x - 8y = 0 linear or nonlinear?

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

Is 3x - y = 6 linear or nonlinear?

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

Is x + y = 0 linear or nonlinear?

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

Is 2x - 3y = 6 linear or nonlinear?

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

Is x = 6 linear or nonlinear?

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

Is y = 1 linear or nonlinear?

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

Is y = x² linear or nonlinear?

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

Is 3x² + 2y = 10 linear or nonlinear?

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

Is 4x² - 6y = 2 linear or nonlinear?

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

Is 5xy - 7 = 10 linear or nonlinear?

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

Is 6yx + 3y = 10 linear or nonlinear?

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

Is (6/x) + 3y = 9 linear or nonlinear?

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

Is 5x + (7/y) = 3 linear or nonlinear?

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

Is 4xy = 10 linear or nonlinear?

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

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Study Notes

Function Evaluation

  • Evaluating f(x) = 3x + 2 for various x-values results in specific outputs: f(4) = 14, f(8) = 26, f(-2) = -4, f(1) - 1 = 4, f(2) + 1 = 9, and f(x + 1) = 3x + 5.
  • For f(x) = 2x², outputs from evaluations include f(3) = 18, f(-4) = 32, f(5) + 1 = 51, and f(-6) - 5 = 67.

Quadratic Function Evaluation

  • Evaluating g(x) = x² - x provides results: g(2) = 2, g(-3) = 12, g(-6) = 42, g(2) - 2 = 0, and g(-1) + 4 = 6.
  • Using g(3b) results in g(3b) = 9b² - 3b.

Function Representation

  • A set of points represents a function if each x-value maps to a single y-value:
    • Yes: {(2, 5), (4, -2), (3, 3), (5, 4), (-2, 5)} and y = x + 3.
    • No: {(6, -1), (-4, 2), (5, 2), (4, 6), (6, 5)} and x = 2.

Domain and Range

  • The domain of a set is the collection of x-values. Example: Domain for {(4, 3), (-1, 4), (3, -2), (-2, 1)} is {4, -1, 3, -2}.
  • The range consists of y-values. For the same set, range is {3, 4, -2, 1}.

Identifying Variables

  • Independent variables correlate with the domain, representing x-values.
  • Dependent variables relate to the range, symbolizing y-values.

Linearity in Equations

  • Equations are classified as linear or nonlinear:
    • Linear equations: 3x + 2y = 9, 5x = 10, 3x = 2, 2y = -4, -5y = 20, 7x - 8y = 0, 3x - y = 6, x + y = 0, 2x - 3y = 6, and x = 6.
    • Nonlinear equations include y = x², 3x² + 2y = 10, 4x² - 6y = 2, 5xy - 7 = 10, 6yx + 3y = 10, (6/x) + 3y = 9, 5x + (7/y) = 3, and 4xy = 10.

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