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 parentheses, such as f(x), where 'x' is the input variable.

Front

How do you write an equation for a scenario involving a fixed cost and a variable cost?

Back

The equation is written as y = fixed cost + (variable cost per unit * number of units). For example, if the fixed cost is $10 and the variable cost is $4 per hour, the equation is y = 10 + 4x.

Front

Evaluate f(2) if f(x) = 3x + 5.

Back

f(2) = 3(2) + 5 = 6 + 5 = 11.

Front

What does the slope represent in a linear function?

Back

The slope represents the rate of change of the function. It indicates how much the output (y) changes for a unit change in the input (x).

Front

If f(x) = 2x + 3, what is f(-1)?

Back

f(-1) = 2(-1) + 3 = -2 + 3 = 1.

Front

What is the y-intercept in the equation y = mx + b?

Back

The y-intercept is the value of y when x = 0. It is represented by 'b' in the equation.

Front

How do you find the value of y in the equation y = 4x - 1 when x = 3?

Back

y = 4(3) - 1 = 12 - 1 = 11.

Front

What is the difference between independent and dependent variables in a function?

Back

The independent variable is the input (x), while the dependent variable is the output (y) that depends on the value of the independent variable.

Front

Evaluate f(-4) if f(x) = 3x + 7.

Back

f(-4) = 3(-4) + 7 = -12 + 7 = -5.

Front

What is the domain of a function?

Back

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