Functions and Direct Variation

Front

What is a function?

Back

A function is a relation where each input (x-value) has exactly one output (y-value).

Front

What is NOT a function?

Back

A relation is NOT a function if at least one input (x-value) has more than one output (y-value).

Front

What does direct variation mean?

Back

Direct variation means that two quantities increase or decrease together at a constant rate, represented by the equation y = kx, where k is a non-zero constant.

Front

If y varies directly as x, and y = 39 when x = 3, what is the constant of variation (k)?

Back

k = y/x = 39/3 = 13.

Front

In a direct variation, if x = 2, what is y when k = 13?

Back

y = kx = 13 * 2 = 26.

Front

How do you determine if a graph represents a function?

Back

A graph represents a function if it passes the vertical line test; no vertical line should intersect the graph more than once.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a graph is a function by checking if any vertical line crosses the graph more than once.

Front

If Trina earns $187.15 for 19 hours of work, how much does she earn per hour?

Back

She earns $187.15 / 19 hours = $9.85 per hour.

Front

If Trina works 40 hours, how much will she earn?

Back

Earnings = hourly rate * hours worked = $9.85 * 40 = $394.

Front

What is the equation for direct variation?

Back

The equation for direct variation is y = kx, where k is the constant of variation.