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Understanding Function Domains and Conditions

Understanding Function Domains and Conditions

Assessment

Interactive Video

Mathematics

9th - 10th Grade

Practice Problem

Hard

Created by

Olivia Brooks

FREE Resource

The video tutorial introduces the concept of the domain of a function, explaining it as the set of input values that produce valid outputs. It covers various examples, including f(x) = x squared, f(x) = 1/x squared, f(x) = sqrt(x-3), f(x) = sqrt(|x|-3), and a piecewise function. The tutorial discusses how to determine the domain by considering conditions like undefined values and non-negative expressions under square roots.

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the domain of a function?

The set of all complex numbers.

The set of all real numbers.

The set of all possible inputs that produce a valid output.

The set of all possible outputs of a function.

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

For the function f(x) = x^2, which of the following is true about its domain?

x cannot be zero.

x must be a complex number.

x must be a positive integer.

x can be any real number.

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Why is f(x) = 1/x^2 undefined at x = 0?

Because the function only accepts negative numbers.

Because the function only accepts positive numbers.

Because zero is not a real number.

Because 1 divided by zero is undefined.

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

For the function f(x) = √(x-3), what must be true for x?

x must be greater than or equal to 3.

x must be a negative number.

x must be less than 3.

x must be a complex number.

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In the function f(x) = √|x-3|, what is the condition for x?

x must be a positive integer.

x must be equal to 3.

x must be less than -3 or greater than 3.

x must be greater than 3.

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

For the function f(x) = 1/√|x-3|, why can't x be 3?

Because it would make the numerator zero.

Because x must be a negative number.

Because it would make the denominator zero.

Because x must be a positive number.

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In the piecewise function where f(x) = 2 if x is even, what is the domain?

All real numbers except 1.

All even numbers.

All odd numbers.

All real numbers.

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