Linear and Non-Linear Functions

How can you identify a linear function from its graph?

• A linear function has a curved graph.

• A linear function can be identified by its straight-line graph.

• A linear function has a variable slope.

• A linear function is represented by a parabolic curve.

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What is a linear function?

• A function that can be represented as a straight line with the form f(x) = mx + b.

• A function that has a constant rate of change and can be represented as a curve.

• A function that can only take positive values and is represented as a parabola.

• A function that has no slope and is represented as a horizontal line.

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What is the significance of the domain and range in functions?

• The domain is the set of all possible output values, while the range is the set of all possible input values.

• The domain of a function is the set of all possible input values (x-values), while the range is the set of all possible output values (y-values).

• The domain and range are irrelevant in understanding the behavior of a function.

• The domain is the set of all values that make the function undefined, while the range is the set of all values that make the function continuous.

What is a piecewise function?

• A function that is defined by different expressions for different intervals of the input variable.

• A function that is continuous and has no breaks.

• A function that can only be represented graphically.

• A function that has a single expression for all input values.

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How do you determine if a function is linear or nonlinear from a table of values?

• Check if the differences between consecutive y-values are constant for equal changes in x-values.

• Look for a quadratic pattern in the y-values.

• Identify if the x-values are in ascending order.

• Determine if the y-values are all positive.

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What is a function?

• A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

• A function is a mathematical operation that combines two or more numbers to produce a single number.

• A function is a type of graph that represents data points in a coordinate system.

• A function is a programming construct that allows for the execution of a block of code multiple times.

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What is a nonlinear function?

• A function that forms a straight line when graphed.

• A function that does not form a straight line when graphed. Its graph can be a curve, a circle, or any other shape that is not a straight line.

• A function that only includes polynomial expressions.

• A function that has a constant rate of change.

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What is an example of a nonlinear function?

• f(x) = 2x + 3

• f(x) = x^2

• f(x) = 5

• f(x) = 3x - 7

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What is the slope of a linear function?

• A measure of its steepness, represented by 'm' in the equation f(x) = mx + b.

• The point where the line crosses the y-axis.

• The distance between two points on the line.

• The angle formed by the line with the x-axis.

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What is an example of a linear function?

• f(x) = 2x + 3

• f(x) = x^2 + 1

• f(x) = 3x - 5

• f(x) = 1/x

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