Linear Functions

Front

What is the equation of a linear function that represents a gym membership with a startup fee and monthly fee?

Back

Y = 40 + 10x, where Y is the total cost and x is the number of months.

Front

What are appropriate outputs for the equation Y = 40 + 10x when x = 0, 1, 2?

Back

$40 (for x=0), $50 (for x=1), $60 (for x=2)...

Front

What does it mean for a relation to be a function?

Back

Every input has only ONE output.

Front

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

Back

The slope represents the rate of change of the function.

Front

How can you determine if a relation is a function using a graph?

Back

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 the significance of the startup fee in the gym membership equation?

Back

It represents the initial cost before any monthly fees are applied.

Front

What does the variable 'x' represent in the equation Y = 40 + 10x?

Back

The variable 'x' represents the number of months of gym membership.

Front

What is the meaning of the term 'rate of change' in a linear function?

Back

It refers to how much the output (Y) changes for a unit change in the input (x).

Front

Can a linear function have a negative slope?

Back

Yes, a linear function can have a negative slope, indicating a decrease in output as input increases.

Front

What is an example of a situation that does not represent a function?

Back

A relation where one input corresponds to multiple outputs, such as a person having multiple phone numbers.