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Excel in math and science

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Algebra

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

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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

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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

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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.

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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,
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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!

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View solution

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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.

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.