Writing and interpreting functions

Front

What does it mean when y varies directly as x?

Back

It means that y is proportional to x, which can be expressed as y = kx, where k is the constant of variation.

Front

If y = 30 when x = 8, what is the constant of variation (k)?

Back

k = y/x = 30/8 = 3.75.

Front

If y varies directly with x and y = 15 when x = 3, what is y when x = 6?

Back

y = kx; k = 15/3 = 5; y = 5 * 6 = 30.

Front

What is the formula for direct variation?

Back

y = kx, where k is the constant of variation.

Front

If z varies directly as r and z = 243 when r = 27, what is the constant of variation (k)?

Back

k = z/r = 243/27 = 9.

Front

If z = 7020 when r = 780, what is the value of z when r = 1?

Back

z = k * r; k = 9; z = 9 * 1 = 9.

Front

What does it mean when a quantity varies inversely?

Back

It means that as one quantity increases, the other decreases, expressed as xy = k.

Front

If the time (t) to build a desk varies inversely with the number of students (s), what is the equation if t = 200 when s = 8?

Back

t = 1600/s.

Front

What is the constant of variation for weight and volume if weight = 14 ounces and volume = 10 cubic inches?

Back

k = weight/volume = 14/10 = 7/5.

Front

If y varies directly as x and y = 15 when x = 3, what is the value of y when x = 4?

Back

k = 15/3 = 5; y = 5 * 4 = 20.