Solving Functions (Function Notation)

Front

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 input variable in parentheses, such as f(x).

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 in place of the variable. For example, to evaluate f(x) = 2x + 3 at x = 4, calculate 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 given output. For example, if f(x) = 10, you would find x such that f(x) = 10.

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 isolate x in an equation?

Back

To isolate x, perform inverse operations to both sides of the equation until x is alone on one side. For example, in the equation 2x + 3 = 7, subtract 3 from both sides, then divide by 2.

Front

If f(x) = -2x - 12, what is f(-5)?

Back

f(-5) = -2(-5) - 12 = 10 - 12 = -2.

Front

How do you find the value of x when f(x) is given?

Back

Set the function equal to the given value and solve for x. For example, if f(x) = 3x + 1 and f(x) = 7, set 3x + 1 = 7 and solve for x.

Front

What is the value of x if f(x) = 3x + 1 and f(x) = 7?

Back

3x + 1 = 7; subtract 1 from both sides: 3x = 6; divide by 3: x = 2.

Front

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

Back

5x - 1 = 19; add 1 to both sides: 5x = 20; divide by 5: x = 4.

Front

What is the output of f(x) = 3x + 1 when x = 2?

Back

f(2) = 3(2) + 1 = 6 + 1 = 7.