Solving Functions (Function Notation)

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What is function notation?

Back

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(4), you would calculate 2(4) + 3 = 11.

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What does it mean to solve for x in a function?

Back

Solving for x in a function means finding the value of x that makes the function equal to a specific output. This often involves rearranging the equation to isolate x.

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If f(x) = 3x + 1, what is f(2)?

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f(2) = 3(2) + 1 = 7.

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What is the inverse of a function?

Back

The inverse of a function f(x) is a function that reverses the effect of f. If f(x) takes an input x and produces an output y, then the inverse function f^(-1)(y) takes y back to x.

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How do you find the value of x when f(x) = k?

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To find the value of x when f(x) = k, set the function equal to k and solve for x. For example, if f(x) = 2x + 3 and k = 7, set 2x + 3 = 7 and solve for x.

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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 the form f(x) = mx + b, where m is the slope and b is the y-intercept.

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If f(x) = 5x - 1, what is the value of x when f(x) = 19?

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Set 5x - 1 = 19. Solving gives x = 4.

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What is the slope of the function f(x) = 2x + 5?

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The slope of the function f(x) = 2x + 5 is 2, which indicates that for every unit increase in x, f(x) increases by 2 units.

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How do you graph a linear function?

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To graph a linear function, identify the y-intercept (b) and the slope (m). Start at the y-intercept on the y-axis, then use the slope to find another point, and draw a straight line through the points.