Functions & Solving Linear Expressions

Front

What is a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Front

How can you tell if a table represents a function?

Back

A table represents a function if each input (x-value) is associated with only one output (y-value). If any x-value is repeated with different y-values, it is not a function.

Front

What does the equation y = mx + b represent in a linear function?

Back

In the equation y = mx + b, 'm' represents the slope of the line, and 'b' represents the y-intercept, where the line crosses the y-axis.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the rise (change in y) over the run (change in x).

Front

What is a linear expression?

Back

A linear expression is an algebraic expression in which the highest power of the variable is one.

Front

How do you calculate the total cost of a service with a fixed fee and a variable charge?

Back

The total cost can be calculated using the equation: Total Cost = Fixed Fee + (Variable Charge per Unit × Number of Units).

Front

If a taxi charges a fixed fee of $4.25 and $2.75 per mile, what is the total cost for 5 miles?

Back

Total Cost = 4.25 + (2.75 × 5) = 4.25 + 13.75 = $18.00.

Front

What does f(x) represent in a function?

Back

f(x) represents the output of the function for a given input x.

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of y when x = 0.

Front

How do you determine the number of rounds you can play for a fixed budget?

Back

To determine the number of rounds, subtract the fixed cost from the total budget and divide by the cost per round.