Comparing Functions

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What is a linear function?

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A linear function is a function that can be graphically represented as a straight line. It has a constant rate of change and can be expressed in 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?

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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 be represented by equations that include exponents, logarithms, or other non-linear terms.

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How do you determine the rate of change in a function?

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The rate of change in a function is determined by calculating the difference in the y-values divided by the difference in the x-values (rise over run) between two points on the graph.

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What is the y-intercept of a function?

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The y-intercept of a function is the point where the graph intersects the y-axis. It is represented as (0, b) in the equation y = mx + b.

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What does it mean for a function to have a greater rate of change?

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A function with a greater rate of change increases or decreases more rapidly than another function. This is often indicated by a steeper slope in the graph.

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

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A linear function will have a constant difference in the y-values for equal intervals in the x-values. If the differences are not constant, the function is nonlinear.

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What is the slope of a line?

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The slope of a line is a measure of its steepness, calculated as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.

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What is the significance of the slope in a linear function?

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The slope indicates the rate of change of the function. A positive slope means the function is increasing, while a negative slope means it is decreasing.

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How can you graph a linear function?

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To graph a linear function, you can plot the y-intercept on the y-axis and use the slope to find another point. Draw a straight line through these points.

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What are some common forms of nonlinear functions?

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Common forms of nonlinear functions include quadratic functions (y = ax^2 + bx + c), exponential functions (y = a * b^x), and logarithmic functions (y = log_b(x)).