Equations as functions (tables)

Front

What is a function?

Back

A function is a relation that assigns exactly one output (y) for each input (x).

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.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y) that the function can produce.

Front

How do you find the value of y in the equation y = x + 3 when x = -2?

Back

Substitute -2 for x: y = -2 + 3 = 1.

Front

What does the equation y = -4 represent graphically?

Back

It represents a horizontal line where the y-value is always -4, regardless of x.

Front

What is an ordered pair in the context of functions?

Back

An ordered pair (x, y) represents a point on the graph of a function, where x is the input and y is the output.

Front

How do you determine the missing value in an ordered pair for the equation y = -2x + 8 when x = 5?

Back

Substitute 5 for x: y = -2(5) + 8 = -10 + 8 = -2.

Front

What is a linear equation?

Back

A linear equation is an equation that forms a straight line when graphed, typically in the form y = mx + b.

Front

What does the slope (m) represent in a linear equation?

Back

The slope represents the rate of change of y with respect to x; it indicates how steep the line is.

Front

What is the y-intercept (b) in a linear equation?

Back

The y-intercept is the value of y when x = 0; it is the point where the line crosses the y-axis.