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Function Transformations (Definition) - Single Transformation Graph to Function

Level 1

This math topic focuses on the skill of identifying single transformations applied to original functions and interpreting their corresponding graphical representations. Each problem presents a graph of a transformed function \( g(x) \) and offers multiple choices to select the correct transformation applied to the initial function \( f(x) \). The transformations include reflections, translations, and vertical or horizontal shifts, testing the learner's ability to understand and analyze function transformations from graphical output.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Function Transformations (Definition) - Single Transformation Graph to Function Worksheet

Function Transformations (Definition) - Single Transformation Graph t...

Which transformed function g(x) is this graph showing?

An svg image showing a math problem

a $A LaTex expression showing f(x) = x\\g(x) = - f(-x)$

b $A LaTex expression showing f(x) = x\\g(x) = f(-x)$

c $A LaTex expression showing f(x) = x\\g(x) = f(x)$

Which transformed function g(x) is this graph showing?

An svg image showing a math problem

a $A LaTex expression showing f(x) = x to the power of 3 \\g(x) = f(-x)$

b $A LaTex expression showing f(x) = x to the power of 3 \\g(x) = - f(-x)$

c $A LaTex expression showing f(x) = x to the power of 3 \\g(x) = f(x)$

Which transformed function g(x) is this graph showing?

An svg image showing a math problem

a $A LaTex expression showing f(x) = x\\g(x) = f(x- 5)$

b $A LaTex expression showing f(x) = x\\g(x) = f(x+ 5)$

c $A LaTex expression showing f(x) = x\\g(x) = f(x)+ 5$

Which transformed function g(x) is this graph showing?

An svg image showing a math problem

a $A LaTex expression showing f(x) = x to the power of 3 \\g(x) = f(x)- 2$

b $A LaTex expression showing f(x) = x to the power of 3 \\g(x) = f(x- 2)$

c $A LaTex expression showing f(x) = x to the power of 3 \\g(x) = f(x)+ 2$

An svg image showing a math problem

Which transformed function g(x) is this graph showing?

a $A LaTex expression showing f(x) = x to the power of 2 \\g(x) = f(x+ 4)$

b $A LaTex expression showing f(x) = x to the power of 2 \\g(x) = f(x- 4)$

Which transformed function g(x) is this graph showing?

An svg image showing a math problem

a $A LaTex expression showing f(x) = x\\g(x) = f(x- 3)$

b $A LaTex expression showing f(x) = x\\g(x) = f(x+ 3)$

c $A LaTex expression showing f(x) = x\\g(x) = f(x)+ 3$

An svg image showing a math problem

Which transformed function g(x) is this graph showing?

a $A LaTex expression showing f(x) = x to the power of 3 \\g(x) = f(x)- 3$

b $A LaTex expression showing f(x) = x to the power of 3 \\g(x) = f(x)+ 3$

Which transformed function g(x) is this graph showing?

An svg image showing a math problem

a $A LaTex expression showing f(x) = x\\g(x) = f(x)$

b $A LaTex expression showing f(x) = x\\g(x) = - f(-x)$

c $A LaTex expression showing f(x) = x\\g(x) = - f(x)$