Linear Functions

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a linear function represent?

Back

The slope of a linear function represents the rate of change of the function. It indicates how much the output value (y) changes for a unit change in the input value (x).

Front

What is the y-intercept in a linear function?

Back

The y-intercept is the value of the function when the input (x) is zero. It is the point where the line crosses the y-axis.

Front

How do you determine if a relation is a function?

Back

A relation is a function if each input value (x) is associated with exactly one output value (y). This can be checked using the vertical line test on its graph.

Front

What is the equation of a linear function that includes a start-up fee and a monthly fee?

Back

The equation can be represented as Y = b + mx, where b is the start-up fee and m is the monthly fee.

Front

If a gym charges a start-up fee of $40 and a monthly fee of $10, what is the output when x = 3?

Back

The output is Y = 40 + 10(3) = 70.

Front

What are appropriate input values for the gym membership function Y = 40 + 10x?

Back

Appropriate input values are non-negative integers: 0, 1, 2, 3, ... (representing the number of months).

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What does it mean if a function is 'not a function'?

Back

It means that there exists at least one input value that corresponds to more than one output value, violating the definition of a function.

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How can you find the output value of a linear function for a given input?

Back

Substitute the input value into the function's equation and solve for the output value.

Front

What is the significance of the equation Y = 40 + 10x in a real-world context?

Back

It models the total cost of joining a gym, where $40 is the initial fee and $10 is the recurring monthly fee.