Algebra 1: Topic 3 (Linear Functions)

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 line represent?

Back

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

Front

What is the y-intercept of a linear function?

Back

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

Front

How do you determine if a function is linear?

Back

A function is linear if it can be expressed in the form f(x) = mx + b, and its graph is a straight line.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a graph represents a function. If a vertical line intersects the graph at more than one point, it is not a function.

Front

What does it mean for a graph to be continuous?

Back

A continuous graph means that there are no breaks, holes, or gaps in the graph. It can be drawn without lifting the pencil from the paper.

Front

What is a transformation in the context of graphing functions?

Back

A transformation refers to changes made to the graph of a function, such as translations, reflections, stretches, or compressions.

Front

What is a vertical translation of a graph?

Back

A vertical translation moves the graph up or down without changing its shape. For example, adding a constant to the function shifts it upward.

Front

What is a horizontal translation of a graph?

Back

A horizontal translation moves the graph left or right. For example, subtracting a constant from the x-value shifts it to the right.

Front

What is a reflection in graphing?

Back

A reflection flips the graph over a specific axis. For example, reflecting over the x-axis changes the sign of the y-values.