Linear or Nonlinear

Front

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. It can have curves, bends, or other shapes, and can be represented by equations that are not in the form of f(x) = mx + b.

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 constant, 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 is the slope in a Linear Function?

Back

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

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What is the y-intercept in a Linear Function?

Back

The y-intercept (b) in a linear function is the value of y when x is 0. It is the point where the line crosses the y-axis.

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.

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What does it mean if a function is represented by a quadratic equation?

Back

If a function is represented by a quadratic equation, it is nonlinear and typically has the form f(x) = ax^2 + bx + c, where a, b, and c are constants.

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What is the graphical representation of a Linear Function?

Back

The graphical representation of a linear function is a straight line that can slope upwards, downwards, or be horizontal.