Writing Equations From A Table & Real-World Situations

Front

What is a function rule?

Back

A function rule is a mathematical expression that describes the relationship between input (independent variable) and output (dependent variable). It often takes the form of an equation.

Front

How do you write a function rule from a real-world situation?

Back

Identify the fixed costs and variable costs, then express the total cost as a function of the number of items or units.

Front

In the equation f(n) = 55 + 4n, what does each term represent?

Back

55 represents the fixed cost (design fee), and 4n represents the variable cost (cost per child multiplied by the number of children).

Front

What does the slope represent in a linear equation?

Back

The slope represents the rate of change of the dependent variable with respect to the independent variable.

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the value of the dependent variable when the independent variable is zero; it represents the starting point of the function.

Front

How can you determine the equation from a table of values?

Back

Identify the pattern in the changes of the dependent variable as the independent variable changes, then use the slope and y-intercept to form the equation.

Front

What does the equation T = 30m + 15 represent in a gym membership context?

Back

T represents the total cost, m represents the number of months, 30 is the monthly fee, and 15 is the initial sign-up fee.

Front

How do you interpret the equation h = 100 - 7s?

Back

This equation indicates that the height of the object decreases by 7 feet for every second that passes, starting from an initial height of 100 feet.

Front

What does the term 'decreasing function' mean?

Back

A decreasing function is one where the output value decreases as the input value increases.

Front

In the equation h = 12 - 2d, what do the coefficients represent?

Back

The coefficient -2 indicates the rate at which the height decreases per day, and 12 is the initial height of the water.