Solving Functions (Function Notation)

Front

What is function notation?

Back

Function notation is a way to represent functions using symbols. It typically uses the letter 'f' followed by parentheses, such as f(x), where 'x' is the input variable.

Front

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, to evaluate f(x) = x^2 + 3 at x = 2, calculate f(2) = 2^2 + 3 = 7.

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 value. For example, if f(x) = 7, find x such that 3x + 1 = 7.

Front

What is the process to find f(0) for a function?

Back

To find f(0), substitute 0 into the function's equation. For example, for f(x) = -3(x - 1), calculate f(0) = -3(0 - 1) = 3.

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How do you set up an equation from function notation?

Back

To set up an equation from function notation, equate the function to a value. For example, if f(x) = 5x - 1 and you want to find x when f(x) = 19, set up the equation 5x - 1 = 19.

Front

What is the value of x if f(x) = 10 and f(x) = 9x + 1?

Back

To find x, set 9x + 1 = 10. Solving gives 9x = 9, so x = 1.

Front

Evaluate f(-2) if f(x) = x^2 + 3.

Back

f(-2) = (-2)^2 + 3 = 4 + 3 = 7.

Front

If f(x) = 3x + 1, what is the value of x when f(x) = 7?

Back

Set 3x + 1 = 7. Solving gives 3x = 6, so x = 2.

Front

How do you find the output of a function for a given input?

Back

To find the output, substitute the input value into the function's equation and simplify. For example, for f(x) = x^2 + 3, if x = 1, then f(1) = 1^2 + 3 = 4.

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What is the significance of the variable in function notation?

Back

The variable in function notation (like x in f(x)) represents the input value for which the function is evaluated.