Linear or Nonlinear

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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 y = 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. It can include quadratic, exponential, logarithmic, and other types of functions.

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How can you identify a linear function from its equation?

Back

A linear function can be identified by its equation being in the form y = mx + b, where m and b are constants. If the highest exponent of the variable is 1, it is linear.

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What is the general form of a quadratic function?

Back

The general form of a quadratic function is y = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

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What does the graph of a linear function look like?

Back

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

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What does the graph of a quadratic function look like?

Back

The graph of a quadratic function is a parabola, which can open upwards or downwards depending on the sign of the coefficient a.

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What is the slope of a linear function?

Back

The slope of a linear function is the ratio of the change in y to the change in x (rise over run) and indicates the steepness of the line.

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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 line crosses the y-axis, represented by the value of b in the equation y = mx + b.

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How can you determine if a function represented by a table is linear?

Back

A function represented by a table is linear if the differences between consecutive y-values are constant for equal intervals of x.

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What is the significance of the highest exponent in a polynomial function?

Back

The highest exponent in a polynomial function determines the degree of the function, which influences its shape and the number of roots it can have.