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

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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Description

Test your understanding of function evaluation, including linear and quadratic functions. This quiz covers concepts such as domain, range, and identifying variables. Engage with various examples and determine the validity of function representations.

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