Domain and Range

What is the definition of 'Domain' in a function?

• The range of all possible output values (y-values) for a function.

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

• The maximum value that a function can take.

• The minimum value that a function can take.

What is the significance of identifying the domain and range of a function?

• It helps in determining the function's maximum and minimum values.

• It allows for the simplification of complex equations.

• Identifying the domain and range helps understand the behavior of the function and the values it can take.

• It is only necessary for polynomial functions.

What is a real-world example of a function with a specific domain and range?

• A function that models the height of a ball thrown in the air, where the domain is the time the ball is in the air and the range is the height of the ball.

• A function that calculates the total cost of items in a shopping cart, where the domain is the number of items and the range is the total cost.

• A function that predicts the weather based on temperature, where the domain is the time of day and the range is the weather conditions.

• A function that determines the speed of a car based on the distance traveled, where the domain is the distance and the range is the speed.

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CCSS.8.F.A.1

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

• By identifying the x-values that the graph covers.

• By identifying the y-values that the graph covers.

• By finding the slope of the graph.

• By calculating the area under the graph.

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What does it mean for a relation to be a function?

• A relation is a function if each input (x-value) is associated with exactly one output (y-value).

• A relation is a function if it has multiple outputs for a single input.

• A relation is a function if it is represented by a straight line on a graph.

• A relation is a function if it contains at least one ordered pair.

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CCSS.8.F.A.1

What is the definition of 'Range' in a function?

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

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

• The range of a function is the difference between the maximum and minimum values of the function.

• The range of a function is the number of elements in the function's domain.

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CCSS.8.F.A.1

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How can you express the range of a function using interval notation?

• (-1, 1) for the range -1 < y < 1.

• [-1, 1] for the range -1 ≤ y ≤ 1.

• (-∞, ∞) for all real numbers.

• {y | -1 < y < 1} for the range -1 < y < 1.

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CCSS.8.F.A.1

CCSS.HSF.IF.B.5

Can a function have a domain that includes negative numbers?

• No, functions can only have positive numbers as their domain.

• Yes, a function can have a domain that includes negative numbers, as long as those values are valid inputs for the function.

• Only certain types of functions can have negative numbers in their domain.

• Negative numbers are not valid inputs for any function.

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CCSS.8.F.A.1

CCSS.HSF.IF.A.1

How can you express the domain of a function using interval notation?

• (-4, 3) for the domain -4 < x < 3.

• [0, 5) for the domain 0 ≤ x < 5.

• (-∞, 2] for the domain x ≤ 2.

• (1, 4) for the domain 1 < x < 4.

What is an example of a function with a limited domain?

• f(x) = sqrt(x), which has a domain of x >= 0

• f(x) = x^2, which has a domain of all real numbers

• f(x) = 1/x, which has a domain of x != 0

• f(x) = sin(x), which has a domain of all real numbers

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