Exploring Adding and Subtracting Rational Expressions

The video tutorial covers linear, quadratic, and exponential functions. It begins with an introduction to these functions, followed by a detailed explanation of linear functions, including their equations, graphing, and properties like domain and range. Next, it delves into quadratic functions, discussing their standard form, graphing, and the concept of a common second difference. Finally, the tutorial explores exponential functions, highlighting their growth patterns, asymptotic behavior, and common ratios.

What is the standard form of a linear equation?

• y = ax^2 + bx + c

• y = mx + b

• y = m/x + b

• y = a * b^x

What does the slope of -2 indicate in the equation y = -2x + 5?

• Rise of 2 units for every 1 unit run

• Rise of 1 unit for every 2 units run

• Fall of 1 unit for every 2 units run

• Fall of 2 units for every 1 unit run

What is the range of a linear function that extends indefinitely?

• All real numbers

• All negative numbers

• All positive numbers

• No real numbers

What is the vertex form of a quadratic function?

• y = a(x-h)^2 + k

• y = ax + bx^2 + c

• y = mx + b

• y = a * b^x

How do you find the vertex of a parabola given the function y = ax^2 + bx + c?

• x = -2a/b

• x = 2a/b

• x = b/2a

• x = -b/2a

What describes the domain of all quadratic functions?

• All positive numbers

• All negative numbers

• All real numbers

• No real numbers

What is the common second difference in a quadratic function's table?

• Addition of the same number

• Subtraction of the same number

• Multiplication by the same number

• Division by the same number

What is the standard form of an exponential function?

• y = mx + b

• y = ax^2 + bx + c

• y = m/x + b

• y = a * b^x

What is the range of an exponential function that never reaches zero?

• y < 0

• y >= 0

• y > 0

• y <= 0

What does a common ratio in an exponential function table indicate?

• Division by the same number

• Addition of the same number

• Multiplication by the same number

• Subtraction of the same number