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 format f(x), where 'f' is the name of the function and 'x' is the input variable.

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How do you evaluate a function at a specific value?

Back

To evaluate a function at a specific value, substitute the value into the function's equation. For example, if f(x) = 2x + 3 and you want to find f(4), substitute 4 for x: f(4) = 2(4) + 3 = 11.

Front

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 value. This often involves rearranging the equation.

Front

If f(x) = 3(3x - 7), what is f(5)?

Back

f(5) = 3(3(5) - 7) = 3(15 - 7) = 3(8) = 24.

Front

What is the process to solve f(n) = 14 for f(n) = 4 - 10n?

Back

Set 4 - 10n = 14. Rearranging gives -10n = 10, so n = -1.

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How do you find the inverse of a function?

Back

To find the inverse of a function, swap the input and output values and solve for the new output. For example, if f(x) = 2x + 3, the inverse would be found by solving x = 2y + 3 for y.

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What is the significance of the domain in a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined. Understanding the domain helps in determining valid inputs.

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What does it mean if a function is linear?

Back

A function is linear if it can be represented by a straight line on a graph. This means 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 graph a linear function?

Back

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.

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What is a constant function?

Back

A constant function is a function that does not change its value regardless of the input. It can be represented as f(x) = c, where c is a constant.