Writing Function Rules from Tables

Front

What is the general form of a linear equation used to represent a real-world situation?

Back

The general form is y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you write a function rule from a word problem involving a fixed fee and a variable cost?

Back

Identify the fixed fee as the y-intercept and the variable cost as the slope in the equation.

Front

In the context of a gym membership, how would you express the total cost after 'm' months if there is a sign-up fee?

Back

C(m) = monthly fee * m + sign-up fee.

Front

What does the slope represent in a linear function?

Back

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

Front

What is the difference between discrete and continuous data?

Back

Discrete data consists of distinct, separate values, while continuous data can take any value within a range.

Front

How can you determine if a function is linear from a table of values?

Back

If the differences between consecutive y-values are constant for equal intervals of x, the function is linear.

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the value of y when x is 0; it represents the starting point of the function.

Front

How do you find the function rule from a set of points?

Back

Use the points to determine the slope (m) and y-intercept (b) to form the equation y = mx + b.

Front

What does the term 'function' mean in mathematics?

Back

A function is a relation that assigns exactly one output for each input.

Front

How do you interpret the equation y = -2x + 10 in a real-world context?

Back

This equation indicates that for every increase of 1 in x, y decreases by 2, starting from 10.