Math Business and Social Science Quiz

Questions and Answers

What does f(x) mean or stand for in the function f(x)= 5x-3?

How do you determine when a graph is a function?

Use a vertical line test.

What are the two main areas that create domain restriction with a function?

Negative values under a square root and zero in a denominator.

What is the slope of the line in the function y=-4x+3?

-4 Signup and view all the answers

What is the equation of the vertical line through the point (-6,7)?

x=-6 Signup and view all the answers

What is the equation of the horizontal line through the point (-6,7)?

y=7 Signup and view all the answers

Give an example where the real world might limit the domain of a function.

Negative values of x would not make sense. Signup and view all the answers

Describe what is meant by the term slope and give an example of its use in the real world.

Slope is a rate of change; for example, it can represent speed in a distance-time graph. Signup and view all the answers

How would you calculate the total amount of interest on a car loan?

Multiply the car payment by the number of payments and subtract the initial cost. Signup and view all the answers

How do you transpose a matrix?

Take each row and write elements down in a column. Signup and view all the answers

What does the notation a23 represent?

Elements of row 2, column 3 of Matrix A. Signup and view all the answers

In order to multiply two matrices, what must be true about the matrices?

Number of columns in the left matrix must equal the number of rows in the right matrix. Signup and view all the answers

What do you need to do to the objective function when setting up the augmented matrix for the simplex method?

Make it equal to zero and have the z variable alone. Signup and view all the answers

When searching for the pivot column using the simplex method, which indicator value do you choose?

Most negative. Signup and view all the answers

How do you know which pivot row to choose in the simplex method?

Choose the smallest quotient from positive values of the pivot column. Signup and view all the answers

Explain how the multiplication principle works when counting outcomes for a probability experiment.

Multiply the number of outcomes at each stage together. Signup and view all the answers

How do you calculate the expected value (rate of return) if you know the probability for each particular rate of return?

Multiply the expected outcome by the probability and add the products together. Signup and view all the answers

Study Notes

Functions and Graphs

f(x) in the function f(x)= 5x-3 represents y.
To determine if a graph is a function, use the vertical line test; one vertical line should intersect the graph at only one point.
Domain restrictions occur when:
- A function has a negative value under a square root.
- A denominator equals zero.

Slope and Lines

The slope of the line in the equation y=-4x+3 is -4.
The equation of a vertical line through the point (-6,7) is x=-6.
The equation of a horizontal line through the point (-6,7) is y=7.

Real World Application of Functions

In real-world scenarios, certain functions may be restricted, for example, negative values of x may not be practical.
Slope represents the rate of change between variables; real-world applications include changes in speed or price over time.

Interest and Loans

To calculate total interest paid on a car loan, multiply the car payment by the number of payments and subtract the initial cost of the car.

Matrices

To transpose a matrix, convert each row into a column.
The notation a23 indicates the elements found in row 2 and column 3 of Matrix A.
To multiply two matrices, the number of columns in the first matrix must equal the number of rows in the second matrix.

Simplex Method

For setting up an augmented matrix for the simplex method, the objective function should be equal to zero, isolating the z variable on one side and moving x and y to the other.
When searching for the pivot column, select the most negative indicator value.
The pivot row is identified by the smallest quotient of positive values from the pivot column divided into the column terms.

Probability

The multiplication principle calculates outcomes in a probability experiment by multiplying the number of outcomes at each stage.
The expected value (rate of return) is calculated by multiplying each expected outcome by its probability and summing the products.

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Description

Test your knowledge on fundamental concepts in mathematics, particularly in the context of business and social sciences. This quiz covers functions, graph analysis, and domain restrictions. Perfect for students looking to reinforce their understanding of these key topics.