Identifying Functions and Proportionality

Front

What is a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Front

How can you identify a function from a set of ordered pairs?

Back

A set of ordered pairs is a function if no two different ordered pairs have the same first element.

Front

What does it mean for y to be directly proportional to x?

Back

It means that as x increases, y increases at a constant rate, and can be expressed as y = kx, where k is a constant.

Front

If y is directly proportional to x and y = 10 when x = 1/2, what is the constant of proportionality (k)?

Back

k = 20.

Front

If y is directly proportional to x and k = 20, what is the value of y when x = 2?

Back

y = 40.

Front

What is a proportional relationship?

Back

A proportional relationship is one where two quantities maintain a constant ratio.

Front

Which equation represents a proportional relationship?

Back

y = kx, where k is a non-zero constant.

Front

What is the difference between proportional and non-proportional relationships?

Back

In proportional relationships, the ratio of y to x is constant; in non-proportional relationships, this ratio changes.

Front

Identify a non-proportional equation: y = 5x, y = -5.6x, y = x + 3, y = 1/2x.

Back

y = x + 3.

Front

What is the definition of similar figures?

Back

Similar figures have the same shape but may differ in size; their corresponding angles are equal and their sides are proportional.