Equations as Functions

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

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) that the function can accept.

Front

What is the range of a function?

Back

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

Front

How do you find the output of a function?

Back

To find the output of a function, substitute the input value into the function's rule and simplify.

Front

What does it mean for a function to be linear?

Back

A linear function is a function that graphs to a straight line and can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the slope of a line?

Back

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

Front

What is a missing value in a function?

Back

A missing value in a function is an unknown output that can be determined by substituting a known input into the function's rule.

Front

How do you determine the output for a given input in a function rule?

Back

To determine the output, replace the input variable in the function rule with the given input value and calculate the result.

Front

What is the function rule for y = 4x?

Back

The function rule y = 4x means that for every input x, the output y is four times the input.

Front

If the input is -1 in the function y = 10x + 7, what is the output?

Back

The output is -3, calculated as y = 10(-1) + 7 = -10 + 7 = -3.