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 an input variable (like x). For example, f(x) represents the output of the function f when the input is 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. For example, if f(x) = 2x + 3, to find f(4), substitute 4 for x: f(4) = 2(4) + 3 = 11.

Front

What does f(-3) mean in function notation?

Back

f(-3) means to evaluate the function f at the input value of -3. It involves substituting -3 into the function's equation.

Front

If f(x) = x^2 + 2x + 5, what is f(-3)?

Back

f(-3) = (-3)^2 + 2(-3) + 5 = 9 - 6 + 5 = 8.

Front

What is the output of g(x) = -4x + 7 when x = -7?

Back

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

Front

How do you find the value of h(t) = (1/2)t + 7 at t = 8?

Back

h(8) = (1/2)(8) + 7 = 4 + 7 = 11.

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. It can take on different values to produce different outputs.

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.

Front

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

Back

A function is undefined at a certain point if substituting that point into the function's equation does not yield a valid output, often due to division by zero or taking the square root of a negative number.

Front

What is the output of f(x) = -2x + 10 when x = -3?

Back

f(-3) = -2(-3) + 10 = 6 + 10 = 16.