Linear relations and Functions (Review #4)

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What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form f(x) = mx + b, where m is the slope and b is the y-intercept.

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What is a nonlinear function?

Back

A nonlinear function is a function that does not form a straight line when graphed. Its rate of change is not constant.

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How can you determine if a set of ordered pairs represents a function?

Back

A set of ordered pairs represents a function if each input (x-value) is associated with exactly one output (y-value).

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What is the vertical line test?

Back

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

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

Back

A relation is a function if every input has a unique output. This means no x-value can correspond to more than one y-value.

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Can a function have the same y-value for different x-values?

Back

Yes, a function can have the same y-value for different x-values, as long as each x-value corresponds to only one y-value.

Front

What is the slope of a linear function?

Back

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

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What is the y-intercept of a linear function?

Back

The y-intercept of a linear function is the point where the graph intersects the y-axis, represented by the value of b in the equation f(x) = mx + b.

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What is an example of a linear function?

Back

An example of a linear function is f(x) = 2x + 3, which has a slope of 2 and a y-intercept of 3.

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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 forms a parabola when graphed.