Function Notation

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What is function notation?

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Function notation is a way to represent a function using symbols. It typically uses the letter 'f' followed by the variable in parentheses, such as f(x), to denote the output of the function for a given input x.

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How do you evaluate a function at a specific value?

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To evaluate a function at a specific value, substitute the value into the function's equation in place of the variable. For example, if f(x) = 2x + 3 and you want to find f(2), substitute 2 for x: f(2) = 2(2) + 3 = 7.

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What does it mean if f(x) = k for some constant k?

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If f(x) = k, it means that the output of the function f for the input x is equal to the constant k. This indicates a specific point on the graph of the function.

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How do you find the x-value when given f(x)?

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To find the x-value when given f(x) = k, set the function equal to k and solve for x. For example, if f(x) = 3x + 1 and f(x) = 7, set 3x + 1 = 7 and solve for x.

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What is the slope-intercept form of a linear function?

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The slope-intercept form of a linear function is given by the equation y = mx + b, where m is the slope and b is the y-intercept.

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How do you find the y-value for a given x in a linear function?

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To find the y-value for a given x in a linear function, substitute the x value into the function's equation and solve for y. For example, if y = 4x - 1 and x = 2, then y = 4(2) - 1 = 7.

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What is the significance of the y-intercept in a linear function?

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The y-intercept is the point where the graph of the function crosses the y-axis. It represents the value of y when x = 0.

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What does it mean for a function to be linear?

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A function is linear if it can be represented by a straight line on a graph. This means it has a constant rate of change, or slope.

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How do you determine if a function is increasing or decreasing?

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A function is increasing if the output values rise as the input values increase, and decreasing if the output values fall as the input values increase. This can be determined by examining the slope of the function.

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What is the domain of a function?

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