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.

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.A.1

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.

Tags

CCSS.HSF.IF.A.2

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.

Tags

CCSS.HSF.IF.A.2

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.

Tags

CCSS.HSF.IF.A.2

Front

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.

Tags

CCSS.HSF.IF.A.2

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.

Tags

CCSS.HSF.IF.A.2

Front

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

Back

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

Tags

CCSS.HSF.IF.A.2

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.

Tags

CCSS.HSF.IF.A.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.

Tags

CCSS.HSF.IF.A.2

Front

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.

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.A.1