Podcast
Questions and Answers
If f(x) = (3 + x) / (x - 3), what is f(a + 2)?
If f(x) = (3 + x) / (x - 3), what is f(a + 2)?
a + 5 / a - 1
Sam is a waiter at a local restaurant where he earns $7 per hour and tips for each person he serves. What function could Sam use to calculate his total earnings for the day?
Sam is a waiter at a local restaurant where he earns $7 per hour and tips for each person he serves. What function could Sam use to calculate his total earnings for the day?
If f(x) = 2x^2 + 5 * sqrt(x - 2), what is f(6)?
If f(x) = 2x^2 + 5 * sqrt(x - 2), what is f(6)?
82
Given the table of values for y = f(x), which statements are true? (Mark all that apply)
Given the table of values for y = f(x), which statements are true? (Mark all that apply)
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The amount of energy it takes to lift a box is a function of which of the following?
The amount of energy it takes to lift a box is a function of which of the following?
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The amount of time it takes to finish a race might be a function of which of the following? (Select one)
The amount of time it takes to finish a race might be a function of which of the following? (Select one)
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If f(x) has values such that f(15) = 8 and f(5) = 6, what are these values?
If f(x) has values such that f(15) = 8 and f(5) = 6, what are these values?
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Regarding the graph described, which statements are true? (Mark all that apply)
Regarding the graph described, which statements are true? (Mark all that apply)
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For the graph mentioned, what is the domain and range?
For the graph mentioned, what is the domain and range?
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If f(x) = 3x + 5 / x, what is f(a + 2)?
If f(x) = 3x + 5 / x, what is f(a + 2)?
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A function is a rule that assigns each value of the _____ variable to exactly one value of the dependent variable.
A function is a rule that assigns each value of the _____ variable to exactly one value of the dependent variable.
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If f(x) = 2(x)^2 + 5 * sqrt(x - 2), what is the domain for f(x)?
If f(x) = 2(x)^2 + 5 * sqrt(x - 2), what is the domain for f(x)?
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If f(x) = 2x^2 + 5 * sqrt(x - 2), what is f(3)?
If f(x) = 2x^2 + 5 * sqrt(x - 2), what is f(3)?
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If f(x) = 3/(x + 2) - sqrt(x - 3), what is f(19)?
If f(x) = 3/(x + 2) - sqrt(x - 3), what is f(19)?
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If f(x) = 3/(x + 2) - sqrt(x - 3), what is f(19)?
If f(x) = 3/(x + 2) - sqrt(x - 3), what is f(19)?
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For the graph provided, what are the true statements? (-2,0)
For the graph provided, what are the true statements? (-2,0)
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If f(2) = 2(x)^2 + 5sqrt(x + 2), what is f(2)?
If f(2) = 2(x)^2 + 5sqrt(x + 2), what is f(2)?
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Study Notes
Understanding Functions
- A function is a rule linking each value of the independent variable to one value of the dependent variable.
- Representation of functions can be shown with equations, tables, or graphs.
Function Evaluations
- For f(x) = (3 + x)/(x - 3), the evaluation of f(a + 2) results in (a + 5)/(a - 1).
- If f(x) = 2x² + 5√(x - 2), then f(6) equals 82.
- Evaluating f(3) for f(x) = 2x² + 5√(x - 2) gives 23.
- The function f(x) = 3/x + 2 - √(x - 3) results in f(19) = -3.9.
Earnings Example
- Sam's earnings model based on hourly wage and tips: E(n) = 5n + 42, where n is the number of people served.
- Sam earns $7 per hour and approximately $5 in tips per person, working 6 hours.
Domain and Range
- The domain of functions may be restricted based on the equation. For example, for f(x) = 2(x)² + 5√(x + 2), the domain includes all real numbers ≥ -2.
- A table of values shows the function's range, where for f(x), the range is not all real numbers but specific output values.
Function Properties
- A function can have a specific graph shape, such as horizontal or vertical lines which may affect its domain and range.
- Graphs can frequently display relationships where domain includes all real numbers, while range may be limited.
Key Mathematical Insights
- For the function f(x) = 3/x, evaluating f(a + 2) gives 3(a + 2) + 5/(a + 2).
- Common evaluations for f are calculated by substituting x values back into the function's equation.
- The weight of an object can be a function of the amount of energy required to lift it.
Important Function Notation
- Using notation like f(x) clarifies interpretations of mathematical relationships.
- Understanding graph behaviors and functional properties helps in dissecting complex equations, particularly their domains and ranges.
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Description
This quiz focuses on understanding functions in mathematics, specifically designed for APEX level 2.1.3. Participants will tackle various problems involving function evaluation and real-life applications of functions through scenarios like earnings calculations.
