Function Review

Front

What is a function?

Back

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

Front

What is the equation of a linear function?

Back

A linear function can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a line represent?

Back

The slope represents the rate of change of the function, indicating how much y changes for a unit change in x.

Front

How can you determine if a relation is a function?

Back

A relation is a function if every input has only one output. If any input corresponds to multiple outputs, it is not a function.

Front

What is a nonlinear function?

Back

A nonlinear function is a function that does not create a straight line when graphed. Examples include quadratic and cubic functions.

Front

What is the slope of the line represented by the equation y = 2x + 3?

Back

The slope is 2, meaning for every 1 unit increase in x, y increases by 2 units.

Front

What is the y-intercept in the equation y = 4x - 5?

Back

The y-intercept is -5, which is the value of y when x = 0.

Front

What does it mean for a graph to not represent a function?

Back

It means that there are at least two points on the graph that have the same x-coordinate but different y-coordinates.

Front

What is the equation for a linear function with a slope of 3 and a y-intercept of 1?

Back

The equation is y = 3x + 1.

Front

What is the rate of change in the context of a real-world scenario?

Back

The rate of change describes how one quantity changes in relation to another, such as speed (distance over time).