4.06-4.09 Analyzing and Creating Graphs of Functions

Front

What is a function in mathematics?

Back

A function is a relation that assigns exactly one output for each input. It can be represented as f(x), where x is the input.

Front

What does the term 'horizontal intercept' mean?

Back

The horizontal intercept (or x-intercept) is the point where a graph crosses the x-axis, indicating the value of x when the output (y) is zero.

Front

What is a vertical intercept?

Back

The vertical intercept (or y-intercept) is the point where a graph crosses the y-axis, indicating the value of y when the input (x) is zero.

Front

How do you determine the maximum value of a function from its graph?

Back

The maximum value of a function is the highest point on the graph. It can be found by identifying the peak of the curve.

Front

What is the average rate of change of a function?

Back

The average rate of change of a function over an interval is the change in the function's value divided by the change in the input value over that interval.

Front

What does it mean for a function to be increasing?

Back

A function is increasing on an interval 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 on an interval if, as the input values increase, the output values decrease.

Front

What is a minimum point on a graph?

Back

A minimum point is the lowest point on the graph of a function, indicating the smallest output value.

Front

How can you identify a constant rate of change in a graph?

Back

A constant rate of change is represented by a straight line on the graph, indicating that the output changes by the same amount for each unit increase in the input.

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.