Analyzing Functions and Graphs

Front

What is a function?

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 is the vertical line test?

Back

The vertical line test is a method to determine if a curve is a graph of a function. If any vertical line intersects the graph at more than one point, then the graph is not a function.

Front

What does a steeper slope indicate in a distance vs time graph?

Back

A steeper slope indicates a faster speed. The steeper the line, the greater the distance covered in a given time.

Front

What does a horizontal line represent in a distance vs time graph?

Back

A horizontal line represents a stationary object, meaning the distance does not change over time.

Front

How can you tell if a graph represents a real-world scenario?

Back

A graph represents a real-world scenario if it accurately reflects the relationships and changes in the quantities involved, such as distance and time.

Front

What does it mean if a graph crosses the x-axis?

Back

If a graph crosses the x-axis, it indicates that the output value (y) is zero at that point, which can represent a specific event in a real-world context.

Front

What is the significance of the starting point in a distance vs time graph?

Back

The starting point indicates the initial position of the object at time zero, which is crucial for understanding the object's movement.

Front

What does it mean if a graph has multiple outputs for a single input?

Back

If a graph has multiple outputs for a single input, it does not represent a function, as each input must correspond to exactly one output.

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 a negative slope indicate in a distance vs time graph?

Back

A negative slope indicates that the object is moving back towards the starting point, or decreasing in distance over time.