Q. Which of the following best describes a 'piecewise function' as mentioned in the passage?
A.
A function defined by different expressions for different intervals.
B.
A function that is continuous everywhere.
C.
A function that has only one expression.
D.
A function that is defined only at discrete points.
Show solution
Solution
A piecewise function is defined by different expressions depending on the interval of the input value.
Correct Answer:
A
— A function defined by different expressions for different intervals.
Learn More →
Q. Which of the following best describes a function that is one-to-one?
A.
Each output is paired with exactly one input.
B.
Each input corresponds to multiple outputs.
C.
The graph is symmetric about the origin.
D.
The function is always increasing.
Show solution
Solution
A one-to-one function has each output paired with exactly one input, meaning it passes the horizontal line test.
Correct Answer:
A
— Each output is paired with exactly one input.
Learn More →
Q. Which of the following best describes a function that is periodic?
A.
It has a constant value.
B.
It repeats its values at regular intervals.
C.
It is always increasing.
D.
It has no maximum or minimum values.
Show solution
Solution
A periodic function is one that repeats its values at regular intervals, such as sine and cosine functions.
Correct Answer:
B
— It repeats its values at regular intervals.
Learn More →
Q. Which of the following best describes the 'slope' of a linear function as mentioned in the passage?
A.
The rate of change of the function.
B.
The maximum value of the function.
C.
The y-intercept of the function.
D.
The area under the curve.
Show solution
Solution
The slope of a linear function indicates the rate of change of the function with respect to x.
Correct Answer:
A
— The rate of change of the function.
Learn More →
Q. Which of the following best describes the end behavior of the function f(x) = -x^4?
A.
Both ends go to positive infinity.
B.
Both ends go to negative infinity.
C.
The left end goes to negative infinity and the right end goes to positive infinity.
D.
The left end goes to positive infinity and the right end goes to negative infinity.
Show solution
Solution
Since the leading coefficient is negative and the degree is even, both ends of the graph will go to negative infinity.
Correct Answer:
B
— Both ends go to negative infinity.
Learn More →
Q. Which of the following describes the end behavior of the graph of a cubic function?
A.
Both ends rise.
B.
Both ends fall.
C.
One end rises and the other falls.
D.
The graph is constant.
Show solution
Solution
A cubic function has one end rising and the other falling, characteristic of odd-degree polynomials.
Correct Answer:
C
— One end rises and the other falls.
Learn More →
Q. Which of the following describes the range of the function f(x) = x^2?
A.
All real numbers.
B.
All positive real numbers.
C.
All non-negative real numbers.
D.
All integers.
Show solution
Solution
The range of f(x) = x^2 is all non-negative real numbers since the output of the function is always zero or positive.
Correct Answer:
C
— All non-negative real numbers.
Learn More →
Q. Which of the following functions has a graph that approaches but never touches the x-axis?
A.
Linear function
B.
Quadratic function
C.
Exponential function
D.
Constant function
Show solution
Solution
An exponential function approaches the x-axis as x approaches negative infinity but never actually touches it.
Correct Answer:
C
— Exponential function
Learn More →
Q. Which of the following functions has a vertical asymptote?
A.
f(x) = x^2 + 1
B.
f(x) = 1/(x - 2)
C.
f(x) = e^x
D.
f(x) = log(x)
Show solution
Solution
The function f(x) = 1/(x - 2) has a vertical asymptote at x = 2, where the function is undefined.
Correct Answer:
B
— f(x) = 1/(x - 2)
Learn More →
Q. Which of the following graphs represents a function that is neither increasing nor decreasing?
A.
A straight line with a positive slope
B.
A straight line with a negative slope
C.
A horizontal line
D.
A parabolic curve opening upwards
Show solution
Solution
A horizontal line represents a function that is constant, meaning it neither increases nor decreases.
Correct Answer:
C
— A horizontal line
Learn More →
Q. Which of the following graphs represents a function that is not one-to-one?
A.
A straight line with a positive slope.
B.
A parabola opening upwards.
C.
A horizontal line.
D.
A line with a negative slope.
Show solution
Solution
A parabola opening upwards is not one-to-one because it fails the horizontal line test; a horizontal line can intersect it at two points.
Correct Answer:
B
— A parabola opening upwards.
Learn More →
Q. Which of the following graphs represents a function that is strictly increasing?
A.
A graph that slopes downward from left to right.
B.
A graph that slopes upward from left to right.
C.
A horizontal line.
D.
A graph that has both increasing and decreasing intervals.
Show solution
Solution
A strictly increasing function is one where, for any two points x1 and x2, if x1 < x2, then f(x1) < f(x2), which is represented by a graph that slopes upward from left to right.
Correct Answer:
B
— A graph that slopes upward from left to right.
Learn More →
Q. Which of the following graphs represents a quadratic function?
A.
A straight line.
B.
A parabola opening upwards or downwards.
C.
A hyperbola.
D.
A circle.
Show solution
Solution
A quadratic function is represented by a parabola, which can open either upwards or downwards.
Correct Answer:
B
— A parabola opening upwards or downwards.
Learn More →
Q. Which of the following is a characteristic of exponential functions?
A.
They have a constant rate of change.
B.
They grow or decay at a constant percentage rate.
C.
They are always positive.
D.
They can be represented by a straight line.
Show solution
Solution
Exponential functions grow or decay at a constant percentage rate, which is a defining characteristic.
Correct Answer:
B
— They grow or decay at a constant percentage rate.
Learn More →
Q. Which of the following is true about the roots of a cubic function?
A.
It can have at most two real roots.
B.
It can have at most three real roots.
C.
It can have no real roots.
D.
It must have at least one real root.
Show solution
Solution
A cubic function can have at most three real roots, and it is guaranteed to have at least one real root due to the Intermediate Value Theorem.
Correct Answer:
B
— It can have at most three real roots.
Learn More →
Q. Which of the following statements about the graph of a function is true if it is continuous everywhere?
A.
It has no breaks or holes.
B.
It must be a polynomial function.
C.
It can only be a linear function.
D.
It must have at least one x-intercept.
Show solution
Solution
A continuous function has no breaks or holes in its graph.
Correct Answer:
A
— It has no breaks or holes.
Learn More →
Q. Which of the following statements about the inverse of a function is true?
A.
The inverse of a function is always a function.
B.
The inverse of a function is symmetric to the original function about the line y = x.
C.
The inverse can only exist for polynomial functions.
D.
The inverse of a function is always linear.
Show solution
Solution
The inverse of a function is symmetric to the original function about the line y = x, provided the original function is one-to-one.
Correct Answer:
B
— The inverse of a function is symmetric to the original function about the line y = x.
Learn More →
Q. Which of the following statements is true about the graph of a function that is periodic?
A.
It repeats its values at regular intervals.
B.
It is always increasing.
C.
It has no maximum or minimum values.
D.
It is a straight line.
Show solution
Solution
A periodic function is characterized by repeating values at regular intervals, such as sine and cosine functions.
Correct Answer:
A
— It repeats its values at regular intervals.
Learn More →
Q. Which of the following statements is true about the inverse of a function?
A.
The inverse of a function is always a function.
B.
The inverse of a function is not necessarily a function.
C.
The inverse of a function is always linear.
D.
The inverse of a function cannot be graphed.
Show solution
Solution
The inverse of a function is a function only if the original function is one-to-one.
Correct Answer:
B
— The inverse of a function is not necessarily a function.
Learn More →
Q. Which of the following statements is true about the roots of a polynomial function?
A.
A polynomial can have at most as many roots as its degree.
B.
All roots of a polynomial are real numbers.
C.
A polynomial of degree n has exactly n distinct roots.
D.
Roots of a polynomial cannot be complex.
Show solution
Solution
A polynomial function can have at most as many roots as its degree, but not all roots need to be real.
Correct Answer:
A
— A polynomial can have at most as many roots as its degree.
Learn More →
Q. Which of the following statements is true regarding the composition of functions?
A.
The composition of two functions is always a function.
B.
The composition of two functions is never a function.
C.
The composition of two functions can be a function or not, depending on the functions involved.
D.
The composition of two functions is always linear.
Show solution
Solution
The composition of two functions can result in a function or not, depending on the nature of the original functions.
Correct Answer:
C
— The composition of two functions can be a function or not, depending on the functions involved.
Learn More →
Q. Which of the following statements is true regarding the inverse of a function?
A.
The inverse of a function is always a function.
B.
The inverse of a function is defined only for linear functions.
C.
The graph of a function and its inverse are symmetric about the line y = x.
D.
The inverse of a function can never be found.
Show solution
Solution
The graph of a function and its inverse are symmetric about the line y = x, which is a key property of inverse functions.
Correct Answer:
C
— The graph of a function and its inverse are symmetric about the line y = x.
Learn More →
Q. Which of the following statements is true regarding the vertical line test for functions?
A.
A vertical line can intersect a graph at more than one point for it to be a function.
B.
A vertical line can intersect a graph at only one point for it to be a function.
C.
A vertical line test is irrelevant for determining functions.
D.
All graphs pass the vertical line test.
Show solution
Solution
For a graph to represent a function, any vertical line drawn must intersect the graph at most once.
Correct Answer:
B
— A vertical line can intersect a graph at only one point for it to be a function.
Learn More →
Q. Which of the following transformations would result in a vertical shift of the graph of the function f(x)?
A.
f(x) + k
B.
f(x + k)
C.
kf(x)
D.
f(kx)
Show solution
Solution
Adding a constant k to the function f(x) results in a vertical shift of the graph.
Correct Answer:
A
— f(x) + k
Learn More →
Q. Which of the following transformations would result in a vertical shift of the graph of the function f(x) = x^2?
A.
f(x) = x^2 + 3
B.
f(x) = 3x^2
C.
f(x) = x^2 - 3
D.
f(x) = 2x^2
Show solution
Solution
Adding a constant to the function, such as f(x) = x^2 + 3, results in a vertical shift upwards.
Correct Answer:
A
— f(x) = x^2 + 3
Learn More →
Showing 61 to 85 of 85 (3 Pages)
Functions & Graphs MCQ & Objective Questions
Understanding "Functions & Graphs" is crucial for students preparing for school and competitive exams in India. This topic forms the backbone of many mathematical concepts and is frequently tested through MCQs and objective questions. Practicing these questions not only enhances conceptual clarity but also boosts confidence, leading to better scores in exams.
What You Will Practise Here
Definition and types of functions: linear, quadratic, polynomial, and exponential.
Graphing techniques: plotting points, understanding slopes, and intercepts.
Key formulas related to functions and their graphs.
Transformations of functions: translations, reflections, and stretches.
Identifying domain and range of functions.
Real-life applications of functions and graphs.
Common graph shapes and their characteristics.
Exam Relevance
"Functions & Graphs" is a significant topic in various examinations, including CBSE, State Boards, NEET, and JEE. Students can expect questions that test their understanding of function properties, graph interpretations, and application of formulas. Common question patterns include multiple-choice questions that require selecting the correct graph or identifying function types based on given equations.
Common Mistakes Students Make
Confusing the domain and range of functions.
Misinterpreting the slope of a line in graph-related questions.
Overlooking transformations when graphing functions.
Failing to identify key points such as intercepts and turning points.
FAQs
Question: What are the different types of functions I need to know for exams?Answer: You should be familiar with linear, quadratic, polynomial, and exponential functions, as they are commonly tested.
Question: How can I improve my graphing skills for the exam?Answer: Regular practice with graphing exercises and understanding the properties of different functions will help improve your skills.
Start solving practice MCQs on Functions & Graphs today to solidify your understanding and excel in your exams. Remember, consistent practice is the key to success!
