Flashcard Linear Functions 2

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a linear function represent?

Back

The slope of a linear function represents the rate of change of the function. It indicates how much the y-value changes for a one-unit increase in the x-value.

Front

What is the y-intercept in a linear function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis. It is represented by the value of b in the function f(x) = mx + b.

Front

How do you determine if a point lies on the graph of a linear function?

Back

To determine if a point (x, y) lies on the graph of a linear function, substitute the x-value into the function and see if the resulting y-value matches the y-value of the point.

Front

What is the difference between a solid line and a dashed line in graphing inequalities?

Back

A solid line indicates that points on the line are included in the solution set (≥ or ≤), while a dashed line indicates that points on the line are not included (> or <).

Front

How do you graph the inequality y > 2x + 1?

Back

To graph y > 2x + 1, first graph the line y = 2x + 1 as a dashed line. Then shade the region above the line, as it represents all points where y is greater than 2x + 1.

Front

What does the term 'solution set' mean in the context of inequalities?

Back

The solution set of an inequality is the set of all values that satisfy the inequality. It can be represented graphically as a shaded region on a graph.

Front

How can you identify the correct graph for a given inequality?

Back

To identify the correct graph for an inequality, determine the boundary line (solid or dashed) and the direction of shading based on the inequality sign.

Front

What is the significance of the inequality sign in graphing?

Back

The inequality sign indicates whether the solution includes the boundary line (≥ or ≤) or excludes it (> or <) and determines the direction of shading.

Front

What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities with the same variables. The solution is the region where the shaded areas of all inequalities overlap.