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Algebra

Function Graphs

Concept Quizzes

Interpreting Graphs of Functions
Translating Graphs
Stretching Graphs
Graphical Transformation - Problem Solving

Challenge Quizzes

Function Graphs: Level 2 Challenges
Function Graphs: Level 4 Challenges

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

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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

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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

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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

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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

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by Brilliant Staff