Writing and interpreting functions

Front

What does it mean for a variable to vary inversely?

Back

When one variable increases, the other decreases, such that their product is constant. For example, if a varies inversely as b, then a * b = k for some constant k.

Front

If a = 12 when b = 4, what is the constant of variation k?

Back

k = a * b = 12 * 4 = 48.

Front

If a varies inversely as b, and a = 12 when b = 4, find a when b = -16.

Back

a = k/b = 48 / -16 = -3.

Front

If the temperature varies inversely as the number of layers of clothing, and the temperature is 20°C when wearing 2 layers, find the temperature when wearing 5 layers.

Back

k = 20 * 2 = 40; Temperature when wearing 5 layers = k / 5 = 40 / 5 = 8°C.

Front

What is the formula for inverse variation?

Back

y = k/x, where k is the constant of variation.

Front

If the cost per person to rent a cabin varies inversely with the number of people, and the cost is $36 when 5 people share, what is the cost when 8 people share?

Back

k = 36 * 5 = 180; Cost per person when 8 share = 180 / 8 = $22.50.

Front

What does it mean for a variable to vary directly?

Back

When one variable increases, the other also increases, such that their ratio is constant. For example, if w varies directly with v, then w/v = k for some constant k.

Front

For a group of objects made of the same material, if the weight varies directly with volume, what is the constant of variation if an object has a volume of 10 cubic inches and weighs 14 ounces?

Back

Constant of variation = weight/volume = 14/10 = 7/5.

Front

If y varies inversely to x and y = 0.5 when x = 4, what is the equation representing this situation?

Back

y = k/x; k = 0.5 * 4 = 2; Therefore, y = 2/x.

Front

How do you find the constant of variation in direct variation problems?

Back

Multiply the known values of the variables to find k.