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Function Graphs

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!

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Concept Quizzes

Interpreting Graphs of Functions
Translating Graphs
Stretching Graphs
Graph Transformation

Challenge Quizzes

Level 2
Level 4

Translating Graphs

The above graph is the result of parallel translation of \(y = x^2.\) If this graph undergoes an additional translation of \(5\) in the positive direction of the \(x\)-axis and an additional translation of \(6\) in the positive direction of the \(y\)-axis, what is the equation of the resulting graph?

\(y = (x+8)^2+11\) \(y = (x-8)^2-11\) \(y = (x+8)^2-11\) \(y = (x-8)^2+11\)

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.

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by Brilliant Staff

If the graph of the above circle with center \((3,5)\) and radius \(4\) undergoes a translation of \(4\) in the positive direction of the \(x\)-axis and \(5\) in the positive direction of the \(y\) axis, what is the equation of the resulting graph in quadratic form?

\(x^2 +y^2+ 14 x + 20 y + 133=0\) \(x^2 +y^2- 14 x - 20 y + 133=0\) \(x^2 +y^2+ 14 x - 20 y + 133=0\) \(x^2 +y^2- 14 x + 20 y + 133=0\)

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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by Brilliant Staff

If the graph of \( y = -8 x^2 -80 x -38\) undergoes a translation of \(-3\) in the positive direction of the \(x\)-axis and \(3\) in the positive direction of the \(y\)-axis, what is the equation of the resulting graph?

\(y = -8x^2-128x+347\) \(y = -8x^2-128x-347\) \(y = -8x^2+128x-347\) \(y = -8x^2+128x+347\)

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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by Brilliant Staff

If the above graph of \( y = 9 x^3\) is the result of a parallel translation of the equation \(y=f(x)\) by \(- 5\) in the positive direction of the \(x\)-axis followed by a translation of \(- 3\) in the positive direction of the \(y\)-axis, what is the equation \(y=f(x)?\)

\(y = -9(x-5)^3+3\) \(y = 9(x+5)^3-3\) \(y = -9(x+5)^3-3\) \(y = 9(x-5)^3+3\)

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!

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by Brilliant Staff

If the graph of \( y = 5 (x-5)^2 + 7\) undergoes a translation of \(3\) in the positive direction of the \(x\) axis and \(-1\) in the positive direction of the \(y\)-axis, what is the equation of the resulting graph?

\(y = 5(x+8)^2+6\) \(y = 5(x-8)^2-6\) \(y = 5(x-8)^2+6\) \(y = 5(x+8)^2-6\)

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

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New user? Sign up

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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.

Courses

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

Translating 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.