Algebra - Intro to Functions Graphing Stories

Front

What is a function in algebra?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Front

What does the graph of a function represent?

Back

The graph of a function represents the relationship between the input values (x-axis) and the output values (y-axis) visually.

Front

What is the significance of the slope in a linear function?

Back

The slope indicates the rate of change of the function; it shows how much the output value changes for a unit change in the input value.

Front

What does it mean for a function to be increasing?

Back

A function is increasing if, as the input values increase, the output values also increase.

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing if, as the input values increase, the output values decrease.

Front

What is a constant function?

Back

A constant function is a function that does not change its value; it has a slope of zero and is represented by a horizontal line.

Front

How can you determine if a graph represents a function?

Back

You can use the vertical line test: if a vertical line intersects the graph at more than one point, it is not a function.

Front

What is a piecewise function?

Back

A piecewise function is a function that is defined by different expressions for different intervals of the input.

Front

What does it mean for a function to have a maximum or minimum value?

Back

A maximum value is the highest point on the graph of the function, while a minimum value is the lowest point.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.