Module 2 Topic 1

Front

What are the key features of functions that increase over their entire domain?

Back

Functions that increase over their entire domain have a positive slope, meaning as the input (x) increases, the output (y) also increases.

Front

What does the y-intercept of a graph represent in a real-world context?

Back

The y-intercept represents the value of the dependent variable when the independent variable is zero, often indicating an initial condition or starting point.

Front

How do you identify the y-intercept from a graph?

Back

The y-intercept is the point where the graph crosses the y-axis, represented as (0, y).

Front

How do you calculate the average rate of change between two points on a graph?

Back

The average rate of change is calculated by taking the difference in the y-values divided by the difference in the x-values between the two points.

Front

What are first differences in a table of values, and how do you calculate them?

Back

First differences are found by subtracting each y-value from the subsequent y-value in a table. They help determine if the relationship is linear or non-linear.

Front

What indicates a linear relationship in a set of data points?

Back

A linear relationship is indicated by constant first differences between consecutive y-values.

Front

What is the significance of a y-intercept of (0, 3) in a graph?

Back

A y-intercept of (0, 3) indicates that when the independent variable is zero, the dependent variable has a value of 3.

Front

What does it mean if a function is described as increasing?

Back

A function is described as increasing if, for any two points in its domain, the output value at the higher input is greater than the output value at the lower input.

Front

How can you determine if a function is linear from its graph?

Back

A function is linear if its graph forms a straight line, indicating a constant rate of change.

Front

What is the formula for calculating the average rate of change between two points (x1, y1) and (x2, y2)?

Back

The formula is (y2 - y1) / (x2 - x1).