Linear Non Linear

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line. It can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is a nonlinear function?

Back

A nonlinear function is a function that does not graph to a straight line. Its graph can be a curve or any shape that is not a straight line.

Front

What is the vertical line test?

Back

The vertical line test is a method used to determine if a graph represents a function. If any vertical line intersects the graph at more than one point, then the graph is not a function.

Front

What is the horizontal line test?

Back

The horizontal line test is used to determine if a function is one-to-one. If any horizontal line intersects the graph at more than one point, then the function is not one-to-one.

Front

What does it mean for a relation to be a function?

Back

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

Front

Can a function have repeated x-values?

Back

No, a function cannot have repeated x-values with different y-values. If an x-value is repeated with different y-values, it is not a function.

Front

What is an example of a linear function?

Back

An example of a linear function is f(x) = 2x + 3, which graphs to a straight line.

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What is an example of a nonlinear function?

Back

An example of a nonlinear function is f(x) = x^2, which graphs to a parabola.

Front

How can you tell if a table represents a function?

Back

You can tell if a table represents a function by checking if each x-value is paired with only one y-value.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the change in y divided by the change in x (rise/run).