Is the Table Linear or Non-Linear

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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.

Front

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, and it can take various forms such as quadratic, exponential, or logarithmic.

Front

How can you identify a linear function from a table of values?

Back

A linear function will have a constant rate of change between the x-values and y-values. If the differences in y-values divided by the differences in x-values are the same, the function is linear.

Front

How can you identify a nonlinear function from a table of values?

Back

A nonlinear function will show varying rates of change between the x-values and y-values. If the differences in y-values divided by the differences in x-values are not constant, the function is nonlinear.

Front

What does the slope of a linear function represent?

Back

The slope of a linear function represents the rate of change of the function. It indicates how much the y-value changes for a unit change in the x-value.

Front

What is the y-intercept in a linear function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis. It is the value of y when x is 0.

Front

Give an example of a linear function.

Back

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

Front

Give an example of a nonlinear function.

Back

An example of a nonlinear function is f(x) = x^2. This function forms a parabola when graphed.

Front

What is the significance of a function being linear or nonlinear in real-world applications?

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Understanding whether a function is linear or nonlinear helps in predicting outcomes and understanding relationships in real-world scenarios, such as in economics, physics, and biology.

Front

What is a constant rate of change?

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A constant rate of change means that for every unit increase in x, the change in y is always the same. This is characteristic of linear functions.