Algebra - 3.1-3.2 Review - Linear Functions

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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.

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How do you write a linear function for a real-world scenario?

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To write a linear function for a real-world scenario, identify the variables involved, determine the fixed costs (y-intercept), and the variable costs (slope). For example, a taxi fare can be modeled as f(x) = mx + b.

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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 output (y) changes for a unit change in the input (x).

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What is the y-intercept in a linear function?

Back

The y-intercept is the value of the function when x = 0. It represents the starting point of the function on the y-axis.

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How do you find the value of a function at a specific point?

Back

To find the value of a function at a specific point, substitute the value of x into the function and simplify.

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What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

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What is the range of a function?

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The range of a function is the set of all possible output values (y-values) that the function can produce.

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How do you determine the domain from a given set of values?

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To determine the domain from a given set of values, list all the unique x-values that are included in the relation.

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What is the difference between a function and a relation?

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A function is a specific type of relation where each input (x-value) is associated with exactly one output (y-value). A relation can have multiple outputs for a single input.

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How do you graph a linear function?

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