Function Notation

Front

What is function notation?

Back

Function notation is a way to represent a function using symbols. It typically uses letters to denote the function (like f, g, h) and parentheses to indicate the input value, e.g., f(x).

Front

How do you evaluate a function at a specific value?

Back

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

Front

What is an independent variable in function notation?

Back

The independent variable is the input value of the function, often represented by x in f(x). It is the value you choose to substitute into the function.

Front

What is a dependent variable in function notation?

Back

The dependent variable is the output value of the function, often represented by f(x). It depends on the value of the independent variable.

Front

If h(t) = \frac{1}{2}t + 7, what is h(8)?

Back

h(8) = \frac{1}{2}(8) + 7 = 4 + 7 = 11.

Front

If g(x) = -4x + 7, what is g(-7)?

Back

g(-7) = -4(-7) + 7 = 28 + 7 = 35.

Front

If f(x) = -x + 3x + 1, what is f(4)?

Back

f(4) = -4 + 3(4) + 1 = -4 + 12 + 1 = 9.

Front

In the expression h(7) = 10, what does 7 represent?

Back

7 is the independent variable, which is the input value for the function h.

Front

What does it mean if a function is undefined at a certain point?

Back

A function is undefined at a certain point if there is no valid output for that input value, often due to division by zero or taking the square root of a negative number.

Front

What is the general form of a linear function?

Back

The general form of a linear function is f(x) = mx + b, where m is the slope and b is the y-intercept.