Waste less time on Facebook — follow Brilliant.

Graphs are visual representations of functions. If you know how to read graphs, you can say a lot about a function just by looking at its graph. Learn this fine art of mathematical divining.

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations,
examples, and problems from the community.

Used and loved by 4 million people

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Your answer seems reasonable. Find out if you're right!

That seems reasonable. Find out if you're right!

Join using Facebook Join using Google

Join using email

New user? Sign up

Existing user? Sign in

Concept Quizzes

Interpreting Graphs of Functions
Translating Graphs
Stretching Graphs
Graph Transformation

Challenge Quizzes

Level 2
Level 4

Stretching Graphs

Given the graph \( y = 4x^2+9 \), how do we obtain the graph of \[ y = 196x^2 +9?\]

Note: The above graph is not drawn to scale.

Stretch with respect to the \(y\)-axis by a factor of \(\dfrac{1}{7}.\) Stretch with respect to the \(y\)-axis by a factor of \(7.\) Stretch with respect to the \(x\)-axis by a factor of \[7.\] Stretch with respect to the \(x\)-axis by a factor of \(\dfrac{1}{7}.\)

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations,
examples, and problems from the community.

Used and loved by 4 million people

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Your answer seems reasonable. Find out if you're right!

That seems reasonable. Find out if you're right!

Join using Facebook Join using Google

Join using email

New user? Sign up

Existing user? Sign in

View solution

View wiki

by Brilliant Staff

What is the equation of the resulting graph after stretching \(y=9(x-4)^2+8\) by a factor of \(\ 5 \) in the \(y\)-direction?

Note: The above graph is not drawn to scale.

\[y=45(x-20)^2+40\] \[y=\frac{9}{5}(x-20)^2+\frac{8}{5}\] \[y=\frac{9}{5}(x-4)^2+\frac{8}{5}\] \[y=45(x-4)^2+40\]

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations,
examples, and problems from the community.

Used and loved by 4 million people

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Your answer seems reasonable. Find out if you're right!

That seems reasonable. Find out if you're right!

Join using Facebook Join using Google

Join using email

New user? Sign up

Existing user? Sign in

View solution

View wiki

by Brilliant Staff

What is the equation of the resulting graph after stretching \(y=7\sin(8\pi x)\) by a factor of \(\frac{1}{8} \) with respect to the \(x\)-axis?

Note: The above graph is not drawn to scale.

\(y=56\sin(64\pi x)\) \(y=7\sin(512\pi x)\) \(y=56\sin(512\pi x)\) \(y=7\sin(64\pi x)\)

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations,
examples, and problems from the community.

Used and loved by 4 million people

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Your answer seems reasonable. Find out if you're right!

That seems reasonable. Find out if you're right!

Join using Facebook Join using Google

Join using email

New user? Sign up

Existing user? Sign in

View solution

View wiki

by Brilliant Staff

If the graph of \(49x^2+9y^2=25\) undergoes stretching by a factor of \(a > 0\) with respect to the \(x\)-axis and stretching by a factor of \(b >0\) with respect to the \(y\)-axis such that the resulting graph is a circle of radius \(5\), what are \(a\) and \(b?\)

\[a=7\] and \[b=3\] \[a=49\] and \[b=9\] \[a=\frac{1}{49}\] and \[b=\frac{1}{9}\] \[a=\frac{1}{7}\] and \[b=\frac{1}{3}\]

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations,
examples, and problems from the community.

Used and loved by 4 million people

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Your answer seems reasonable. Find out if you're right!

That seems reasonable. Find out if you're right!

Join using Facebook Join using Google

Join using email

New user? Sign up

Existing user? Sign in

View solution

View wiki

by Brilliant Staff

What is the equation of the resulting graph after stretching \(y=-8x^2+9x+6\) by a factor of \(\frac{1}{6} \) horizontally and by a factor of \(2\) vertically?

Note: The above graph is not drawn to scale.

\(y=576x^2-108x-12\) \(y=-576x^2+108x+6\) \(y=576x^2+108x+12\) \(y=-576x^2+108x+12\)

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations,
examples, and problems from the community.

Used and loved by 4 million people

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Your answer seems reasonable. Find out if you're right!

That seems reasonable. Find out if you're right!

Join using Facebook Join using Google

Join using email

New user? Sign up

Existing user? Sign in

View solution

View wiki

by Brilliant Staff

Waste less time on Facebook — follow Brilliant.

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations, examples, and problems from the community.

Used and loved by 4 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.

Featured

Topics

Community

100 Day Summer Challenge

Function Graphs

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations, examples, and problems from the community.

Used and loved by 4 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.

Concept Quizzes

Challenge Quizzes

Stretching Graphs

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations, examples, and problems from the community.

Used and loved by 4 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations, examples, and problems from the community.

Used and loved by 4 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations, examples, and problems from the community.

Used and loved by 4 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations, examples, and problems from the community.

Used and loved by 4 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations, examples, and problems from the community.

Used and loved by 4 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.

Master advanced concepts through explanations,
examples, and problems from the community.

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Master advanced concepts through explanations,
examples, and problems from the community.

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Master advanced concepts through explanations,
examples, and problems from the community.

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Master advanced concepts through explanations,
examples, and problems from the community.

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Master advanced concepts through explanations,
examples, and problems from the community.

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Master advanced concepts through explanations,
examples, and problems from the community.

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Master advanced concepts through explanations,
examples, and problems from the community.

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.