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

Evaluate f(-5) if f(x) = -2x - 12.

Back

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

Front

If f(x) = -4 + \frac{x}{3}, what is the value of x when f(x) = 0?

Back

0 = -4 + \frac{x}{3} => \frac{x}{3} = 4 => x = 12.

Front

For the function f(n) = 4 - 10n, what is the value of n when f(n) = 14?

Back

14 = 4 - 10n => 10n = 4 - 14 => 10n = -10 => n = -1.

Front

Find f(0) for the function f(x) = -3(x - 1).

Back

f(0) = -3(0 - 1) = -3(-1) = 3.

Front

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

Back

19 = 5x - 1 => 5x = 20 => x = 4.

Front

What does it mean for a function to be linear?

Back

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.

Front

What is the slope of the function f(x) = -2x + 3?

Back

The slope is -2, which indicates the line falls as x increases.

Front

How do you find the y-intercept of a function?

Back

To find the y-intercept, set x = 0 in the function and solve for f(0).

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.