8th Grade Math Functions Review

Front

What is a function in mathematics?

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 determine if a set of values represents a function?

Back

A set of values represents a function if no two ordered pairs have the same first element (input) with different second elements (outputs).

Front

What is the rate of change in a linear function?

Back

The rate of change in a linear function is the ratio of the change in the output value to the change in the input value, often represented as 'rise over run'.

Front

What does the initial value of a linear equation represent?

Back

The initial value of a linear equation represents the y-intercept, which is the value of y when x is 0.

Front

How do you write the equation of a line given a rate of change and an initial value?

Back

The equation of a line can be written in the form y = mx + b, where m is the rate of change and b is the initial value.

Front

What is the slope of the line represented by the equation y = 3x + 2?

Back

The slope of the line is 3, which indicates a rate of change of 3 units in y for every 1 unit increase in x.

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, indicating the output value when the input is zero.

Front

How can you identify a function from a graph?

Back

You can identify a function from a graph using the vertical line test: if a vertical line intersects the graph at more than one point, it is not a function.

Front

What is the formula for calculating the total cost in a service-based business?

Back

The total cost can be calculated using the formula: Total Cost = (Hourly Rate * Hours Worked) + Fixed Fees.

Front

What does it mean for a graph to be 'not a function'?

Back

A graph is 'not a function' if there are multiple outputs (y-values) for a single input (x-value).