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
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If f(x) = 3x + 2, find f(2) + 1
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If f(x) = 3x + 2, find f(x + 1)
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If g(x) = x² - x, find g(2)
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If g(x) = x² - x, find g(-3)
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If g(x) = x² - x, find g(-6)
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If g(x) = x² - x, find g(2) - 2
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If g(x) = x² - x, find g(-1) + 4
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If g(x) = x² - x, find g(3b)
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If f(x) = 2x², find f(3)
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If f(x) = 2x², find f(-4)
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If f(x) = 2x², find f(5) + 1
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If f(x) = 2x², find f(-6) - 5
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If g(x) = 3x² + 2x - 1, find g(0)
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If g(x) = 3x² + 2x - 1, find g(2)
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If g(x) = 3x² + 2x - 1, find g(-3)
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If g(x) = 3x² + 2x - 1, find g(-3) + 2
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Does this represent a function: {(2, 5), (4, -2), (3, 3), (5, 4), (-2, 5)}?
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Does this represent a function: {(6, -1), (-4, 2), (5, 2), (4, 6), (6, 5)}?
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Does this represent a function: y = x + 3?
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Does this represent a function: x = 2?
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Does this represent a function: y = 1?
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Does this represent a function: y = -3?
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Does this represent a function: a horizontal line?
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Does this represent a function: a vertical line?
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Does this represent a function: a table with a repeated x-value?
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Does this represent a function: a table with no repeating x-values?
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What is the domain?
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What is the range?
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Find the domain for: {(4, 3), (-1, 4), (3, -2), (-2, 1)}
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Find the range for: {(4, 3), (-1, 4), (3, -2), (-2, 1)}
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Find the domain for: {(0, 9), (0, 8), (1, 2), (4, 3)}
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Find the range for: {(0, 9), (0, 8), (1, 2), (4, 3)}
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Find the domain for: {(3, 1), (2, 3), (3, 2), (2, 1)}
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Find the range for: {(3, 1), (2, 3), (3, 2), (2, 1)}
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What are independent variables?
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What are dependent variables?
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Is 3x + 2y = 9 linear or nonlinear?
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Is 5x = 10 linear or nonlinear?
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Is 3x = 2 linear or nonlinear?
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Is 2y = -4 linear or nonlinear?
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Is -5y = 20 linear or nonlinear?
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Is 7x - 8y = 0 linear or nonlinear?
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Is 3x - y = 6 linear or nonlinear?
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Is x + y = 0 linear or nonlinear?
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Is 2x - 3y = 6 linear or nonlinear?
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Is x = 6 linear or nonlinear?
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Is y = 1 linear or nonlinear?
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Is y = x² linear or nonlinear?
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Is 3x² + 2y = 10 linear or nonlinear?
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Is 4x² - 6y = 2 linear or nonlinear?
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Is 5xy - 7 = 10 linear or nonlinear?
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Is 6yx + 3y = 10 linear or nonlinear?
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Is (6/x) + 3y = 9 linear or nonlinear?
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Is 5x + (7/y) = 3 linear or nonlinear?
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Is 4xy = 10 linear or nonlinear?
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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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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.
