# Quiz: Test your H-level Knowledge of Properties of Functions!

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Explore your understanding of functions with this engaging properties of functions quiz focusing on their essential properties. The quiz comprises ten easy questions designed to test your knowledge of various aspects of functions. From domains and ranges to compositions and symmetry, these questions cover key concepts that form the foundation of function theory.
In this quiz, you'll encounter questions about the properties of functions, such as identifying true statements about domains, recognizing identical functions, determining ranges, and understanding symmetry. The questions are multiple-choice, allowing you to choose from four options for each. After attempting the quiz, you can review your Read moreanswers and read short explanations to solidify your understanding of the correct concepts.
Whether you're a student aiming to reinforce your learning or an enthusiast seeking to sharpen your math skills, the Properties of Functions Quiz offers an excellent opportunity to grasp fundamental principles in a fun and interactive way.

• 1.

### Which of the following is true about the domain of a function?

• A.

It can be empty.

• B.

It must be positive.

• C.

It must be whole numbers.

• D.

It is always negative.

A. It can be empty.
Explanation
The domain of a function can indeed be an empty set. This can happen when there are no valid inputs for which the function produces an output

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• 2.

### If two functions have the same domain and their outputs are equal for every input, they are called:

• A.

Inverse functions

• B.

Identical functions

• C.

Parallel functions

• D.

Composite functions

B. Identical functions
Explanation
If two functions have the same outputs for every input, they are considered identical functions

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• 3.

### Find the range of the following function f(x) = 2x + 3?

• A.

All real numbers

• B.

Positive real numbers

• C.

Negative real numbers

• D.

Integers

A. All real numbers
Explanation
The function f(x) = 2x + 3 is a linear function, and its range encompasses all real numbers

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• 4.

### If a function passes the horizontal line test, it means:

• A.

It's a linear function.

• B.

It's a one-to-one function.

• C.

It's an odd function.

• D.

It's not a polynomial.

B. It's a one-to-one function.
Explanation
Passing the horizontal line test indicates that the function is one-to-one, meaning that each input maps to a unique output

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• 5.

### The composition of two functions f and g is denoted by:

• A.

F(x) * g(x)

• B.

F(g(x))

• C.

F / g

• D.

F + g

B. F(g(x))
Explanation
The composition of two functions f and g is denoted by f(g(x)), which means applying the function g first and then applying f to the result

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• 6.

### The function f(x) = x^2 is:

• A.

Linear

• B.

Odd

• C.

Even

• D.

Constant

C. Even
Explanation
The function f(x) = x^2 is an even function because it is symmetric about the y-axis.

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• 7.

### If f(x) = 3x + 2 and g(x) = x - 5, what is (f ∘ g)(x)?

• A.

2x - 3

• B.

4x - 3

• C.

3x - 7

• D.

3x - 3

C. 3x - 7
Explanation
The composition (f ∘ g)(x) means applying function g first and then applying f In this case, it results in 3x - 7.

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• 8.

### The point where a function intersects the y-axis is called the:

• A.

Origin

• B.

Vertex

• C.

Focus

• D.

Y-intercept

D. Y-intercept
Explanation
The point where a function intersects the y-axis is known as the y-intercept.

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• 9.

### If x is a set that contains an integer which is neither negative nor positive then the set x is

• A.

Empty

• B.

Non-empty

• C.

Finite

• D.

Both Non- empty and Finite

D. Both Non- empty and Finite
Explanation
The non-empty and finite set is set {0}.

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• 10.

### The vertical line test is used to determine:

• A.

If a function is odd or even

• B.

If a function is continuous

• C.

If a function has a vertical asymptote

• D.

If a relation is a function

D. If a relation is a function
Explanation
The vertical line test is used to determine whether a relation is a function. If any vertical line intersects the graph of the relation in more than one point, the relation is not a function.

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• Current Version
• Aug 18, 2023
Quiz Edited by
ProProfs Editorial Team
• Aug 18, 2023
Quiz Created by
Surajit Dey

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