Understanding Linear Functions: Increasing or Decreasing

The video tutorial explains how to determine if a linear function is increasing or decreasing by analyzing the slope. It covers the standard form of linear functions, F(x) = mx + b, where m is the slope and b is the y-intercept. A positive slope indicates an increasing function, while a negative slope indicates a decreasing function. The tutorial includes examples of graphing linear functions, highlighting how changes in x and y values relate to the slope. It provides a detailed analysis of two specific functions, demonstrating how to interpret their slopes and y-intercepts on a graph.

What is the general form of a linear function?

• f(x) = ax^2 + bx + c

• f(x) = mx + b

• f(x) = a/x + b

• f(x) = ax^3 + bx^2 + cx + d

How can you determine if a linear function is increasing?

• The y-intercept is zero.

• The slope is positive.

• The slope is negative.

• The slope is zero.

What does a negative slope indicate about a linear function?

• The function is decreasing.

• The function is undefined.

• The function is increasing.

• The function is constant.

For the function f(x) = -2x + 7, what is the y-intercept?

• 7

• 1

• -2

• 0

In the function f(x) = 3x + 1, what does the slope of 3 indicate?

• The function is increasing.

• The function is constant.

• The function is decreasing.

• The function is undefined.

What happens to the y-value as x increases in the function f(x) = 3x + 1?

• Y decreases by 1.

• Y remains constant.

• Y increases by 3.

• Y decreases by 3.

What is the y-intercept of the function f(x) = 3x + 1?

• 0

• 1

• -1

• 3

How does the graph of a decreasing linear function appear?

• It goes uphill from left to right.

• It is a vertical line.

• It is a horizontal line.

• It goes downhill from left to right.

What is the effect of a positive slope on the graph of a linear function?

• The graph is a horizontal line.

• The graph is a vertical line.

• The graph goes downhill from left to right.

• The graph goes uphill from left to right.

What is the relationship between the change in y and the change in x for a slope of 3?

• Y decreases by 1 for every increase of 3 in x.

• Y decreases by 3 for every increase of 1 in x.

• Y remains constant as x changes.

• Y increases by 3 for every increase of 1 in x.