Functions and Their Evaluations

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Questions and Answers

What is the best fitting model for the flu case data based on the coefficients of determination?

Linear model (correct)

Exponential model (correct)

Quadratic model (correct)

None of the above

The range of points scored by the RBRHS Varsity Basketball team is calculated by finding the difference between the highest and lowest scores.

True

How many points did the team score in their last game if their z-score is 1.1?

Expected score calculation would yield a specific number based on the mean and standard deviation.

The IQR (interquartile range) is calculated as the difference between Q3 and Q______.

1 Signup and view all the answers

What percentage of the scores would you expect to be between 79 and 89?

68% Signup and view all the answers

Match the following statistics with their correct definitions:

Mean = Average of the data Median = Middle value when data is ordered Mode = Most frequently occurring value Range = Difference between maximum and minimum Signup and view all the answers

A curved test score will always increase the mean score of the class.

False Signup and view all the answers

What is the mean score of Ms. Lenhard's class based on the given grades?

79.44 (example for calculation, actual number might differ) Signup and view all the answers

What is the total amount collected from ticket sales if 350 tickets were sold at $5.00 each?

$1,450 Signup and view all the answers

A box plot provides information on the mean, median, and mode of a dataset.

False Signup and view all the answers

How much money will be in the account after 9 years if $500 is deposited with an annual compound interest rate of 8%?

$1,000.50 Signup and view all the answers

The exponential decay model for a car that depreciates 15% each year can be represented as $y = 15000 (______)^x$ where x is the number of years.

0.85 Signup and view all the answers

Match the following variables with their corresponding definitions:

y = The final value after depreciation or growth x = The time in years A(b) = The earnings from the first payment option B(b) = The earnings from the second payment option Signup and view all the answers

Which of the following is the correct function for Option A in Lucy's apple picking scenario?

A(b) = 1.50b Signup and view all the answers

What is the interquartile range of a dataset represented in a box plot?

The interquartile range is the difference between the upper quartile and lower quartile. Signup and view all the answers

The series of values $, 2, 12, 62, ext{...}$ can be expressed as $y = imes ^{(x-1)}$.

5 Signup and view all the answers

Which of the following sets of pairs represents a function?

{(3, 7), (3, 7), (7, 11)} Signup and view all the answers

The expression g(x) = -3x + 1 represents a function.

True Signup and view all the answers

Evaluate g(10) for the function g(x) = -3x + 1.

-29 Signup and view all the answers

To represent the slope of the line y = 3x - 2, fill in the blank: The slope is ___

3 Signup and view all the answers

Match the following expressions to the variable they solve for:

h = (P/2) - w = Solve for w l = P/2 - w = Solve for l y = (8x + 12)/4 = Solve for y x = (2h)/4 = Solve for h Signup and view all the answers

What is the solution to the equation 8x - 4y = -12 for y?

y = -2x + 3 Signup and view all the answers

What is the slope of the line represented by the equation y = 3x - 2?

3 Signup and view all the answers

The system of equations 2x + 5y = 20 is equivalent to y = (-2/5)x + 4.

True Signup and view all the answers

Study Notes

Topic 1: Functions

Functions are relationships where each input has exactly one output. A set of ordered pairs (x, y) can be determined as a function if there are no repeated x-values.
Assessing if a set of points forms a function requires checking for repeated x-coordinates.

Evaluating Function Expressions

To evaluate functions, substitute the given input value into the function's equation.
Examples of functions include g(x) = -3x + 1 and f(x) = -x + 2

Finding Values for Functions

To solve for a variable within a function, substitute the known quantity (f(x), or g(x), or h(x)) into the expression and solve for the other variable (x)
Finding x given a specific output value involves solving the equation after replacing the known output with the corresponding expression

Graphs of Functions

Analyze graphs to determine function values at specific points.
Analyze graphs to define domain/range
identify x-intercepts/y-intercepts, and changes in behavior.

Topic 2: Linear Equations

Graphing linear equations involves plotting the y-intercept and using the slope to find additional points.
Slope-intercept form is: y = mx + b , where 'm' is the slope and 'b' is the y-intercept.
Determining slope and y- intercept. This involves calculating the change in y divided by the change in x, which represents slope.
Finding the y-intercept and using slope-intercept to write an equation.

Topic 3: Literal Equations

Solve equations for a specified variable by isolating that variable on one side of the equation.

Topic 4: Linear Inequalities

Sketching the graph involves plotting a line and shading regions above or below the line, indicating the inequality's solution set.
The solution to a linear inequality can be shown using a shaded area on a coordinate plane
Determine how to solve linear inequalities by using inequalities including the greater than, greater than or equal to, less than, less than or equal to signs

Topic 5: Exponential Functions

Exponential functions are mathematical models that change output proportionally.
Graphing exponential functions involves plotting points to depict their pattern of growth or decay.
Determine or write an equation given a series of points to determine the pattern of growth/decline

Topic 6: Statistics

Data analysis involves calculating measures of central tendency (mean, median, mode) and spread (range, interquartile range).
Create graphs for statistical analysis (box plot).
Determine how the different measurements influence the shape, pattern, and behavior of the data
Correlation and best fit modelling

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Description

This quiz covers the fundamental concepts of functions, including their definitions, evaluation methods, solving for variables, and graph analysis. Test your knowledge on identifying functions from sets of ordered pairs, evaluating expressions, and interpreting graphs to determine domain and range.