Domain and Range

Front

What is the definition of domain in mathematics?

Back

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

Front

What is the definition of range in mathematics?

Back

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

Front

What does it mean for a function to have a range of all real numbers greater than or equal to -6?

Back

It means that the lowest output value of the function is -6, and it can take any value above -6.

Front

If a function has a domain of all real numbers greater than or equal to 0, what does this imply?

Back

It implies that the function can accept any input value starting from 0 and going upwards.

Front

What is the maximum height of a projectile?

Back

The maximum height is the highest point reached by the projectile during its motion.

Front

How do you determine the domain of a function from its graph?

Back

The domain can be determined by identifying the x-values for which the graph exists.

Front

How do you determine the range of a function from its graph?

Back

The range can be determined by identifying the y-values that the graph reaches.

Front

What is an example of a function with a domain of all real numbers?

Back

The function f(x) = x is an example, as it can accept any real number as input.

Front

What is an example of a function with a range of all real numbers between 2 and 4?

Back

The function f(x) = 2 + (2 * sin(x)) for x in [0, 2π] can have a range of [2, 4].

Front

What is the significance of the vertex in a parabolic graph?

Back

The vertex represents the maximum or minimum point of the parabola, depending on its orientation.