Solving Functions (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), where 'x' is the input value.

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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, to evaluate f(x) = 2x + 3 at x = 4, calculate f(4) = 2(4) + 3 = 11.

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What does it mean for a function to be linear?

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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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What is the slope of a linear function?

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The slope of a linear function is a measure of how steep the line is. It is calculated as the change in the y-value divided by the change in the x-value (rise/run).

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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 of the function crosses the y-axis. It occurs when x = 0.

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How do you find the x-intercept of a function?

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To find the x-intercept of a function, set f(x) = 0 and solve for x. The x-intercept is the point where the graph crosses the x-axis.

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What is the difference between independent and dependent variables?

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The independent variable is the input of a function (often x), while the dependent variable is the output (often f(x)). The value of the dependent variable depends on the value of the independent variable.

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What is a function's domain?

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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.

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What is a function's range?

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

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How do you solve for x in a function equation?

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To solve for x in a function equation, isolate x on one side of the equation using algebraic operations. For example, in f(x) = 2x + 3, to find x when f(x) = 7, set 7 = 2x + 3 and solve for x.