Understanding Functions and Graphs

The video tutorial explains the concept of functions, emphasizing that each input has one output. It introduces the vertical line test to determine if a graph represents a function. The tutorial categorizes functions as increasing, decreasing, or constant, and demonstrates how to interpret graphs to tell stories. Real-life scenarios, such as walking away from home, are used to illustrate these concepts, showing how graphs can represent different situations.

What is a key characteristic of a function in terms of inputs and outputs?

• Every output has no inputs.

• Every input has one output.

• Every output has multiple inputs.

• Every input has multiple outputs.

What does the vertical line test determine about a graph?

• If the graph is horizontal.

• If the graph is a function.

• If the graph is increasing.

• If the graph is decreasing.

How can you describe a function that rises as you move from left to right on a graph?

• Increasing function

• Constant function

• Non-linear function

• Decreasing function

What type of function is represented by a line that goes straight across a graph?

• Exponential function

• Increasing function

• Decreasing function

• Constant function

What does a constant function indicate about the output value?

• The output value is increasing.

• The output value is decreasing.

• The output value is constant.

• The output value is variable.

In the context of a graph, what does an increasing section tell us about a journey?

• You are moving closer to home.

• You are lost.

• You are moving away from home.

• You are staying at home.

What might a flat section on a graph indicate about your movement?

• You are moving in circles.

• You have stopped moving.

• You are moving slowly.

• You are moving quickly.

What does a decreasing section on a graph suggest about your distance from home?

• You are getting further from home.

• You are getting closer to home.

• You are staying at home.

• You are moving in a different direction.

How can a steeper line on a graph be interpreted in terms of speed?

• You are moving slower.

• You are moving at a constant speed.

• You are moving faster.

• You are not moving.

What can graphs help us understand about real-world situations?

• They show random data.

• They are only for scientific use.

• They only show mathematical equations.

• They tell stories and explain situations.