Alg 1 Desmos Unit 4 Describing Functions Review

Front

What is the definition of the domain of a function?

Back

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

Front

What is the definition of 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 determine the average rate of change of a function over an interval?

Back

The average rate of change of a function over an interval [a, b] is calculated using the formula: \( \frac{f(b) - f(a)}{b - a} \).

Front

What does the notation \( h(t) \) represent in a function?

Back

The notation \( h(t) \) represents a function named 'h' with 't' as the independent variable.

Front

What is an inequality that describes the domain of a function?

Back

An inequality that describes the domain of a function specifies the range of input values (x-values) for which the function is valid.

Front

What is an inequality that describes the range of a function?

Back

An inequality that describes the range of a function specifies the possible output values (y-values) that the function can take.

Front

If a function has a domain of \( -3 \le t \le 5 \), what does this mean?

Back

This means that the function is defined for all values of 't' from -3 to 5, inclusive.

Front

If a function has a range of \( -3 \le h(t) \le 4 \), what does this mean?

Back

This means that the output values of the function 'h(t)' are between -3 and 4, inclusive.

Front

What is the average rate of change of Austin's function from 3 to 9 minutes if the output changes from 1 to 4?

Back

The average rate of change is \( \frac{4 - 1}{9 - 3} = \frac{3}{6} = 0.5 \).

Front

What is the average rate of change of Austin's function from 9 to 15 minutes if the output changes from 4 to 6?

Back

The average rate of change is \( \frac{6 - 4}{15 - 9} = \frac{2}{6} = \frac{1}{3} \).