APEX 2.1.3 Quiz: Understanding Functions

Questions and Answers

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?

E(n) = 7n + 42

E(n) = 5n + 42 (correct)

E(n) = 5n + 36

E(n) = 5n + 40

If f(x) = 2x^2 + 5 * sqrt(x - 2), what is f(6)?

Given the table of values for y = f(x), which statements are true? (Mark all that apply)

f(-3) = 2 Signup and view all the answers

The amount of energy it takes to lift a box is a function of which of the following?

the weight of objects in the box Signup and view all the answers

The amount of time it takes to finish a race might be a function of which of the following? (Select one)

The distance of the race Signup and view all the answers

If f(x) has values such that f(15) = 8 and f(5) = 6, what are these values?

f(15) = 8; f(5) = 6 Signup and view all the answers

Regarding the graph described, which statements are true? (Mark all that apply)

The equation of this line is x = 3. Signup and view all the answers

For the graph mentioned, what is the domain and range?

The domain is all real numbers; the range is the set {-5}. Signup and view all the answers

If f(x) = 3x + 5 / x, what is f(a + 2)?

3(a + 2) + 5 / (a + 2) Signup and view all the answers

A function is a rule that assigns each value of the _____ variable to exactly one value of the dependent variable.

Independent Signup and view all the answers

If f(x) = 2(x)^2 + 5 * sqrt(x - 2), what is the domain for f(x)?

All real numbers greater than or equal to -2 Signup and view all the answers

If f(x) = 2x^2 + 5 * sqrt(x - 2), what is f(3)?

23 Signup and view all the answers

If f(x) = 3/(x + 2) - sqrt(x - 3), what is f(19)?

-1.67 Signup and view all the answers

If f(x) = 3/(x + 2) - sqrt(x - 3), what is f(19)?

-3.9 Signup and view all the answers

For the graph provided, what are the true statements? (-2,0)

The range is the set of all real numbers greater than or equal to zero; the domain is the set of all real numbers. Signup and view all the answers

If f(2) = 2(x)^2 + 5sqrt(x + 2), what is f(2)?

18 Signup and view all the answers

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.