Function Transformations (Definition) - Single Transformation Graph to Definition

Level 1

This topic focuses on understanding single transformations of functions through graph analysis. Students will identify and describe transformations such as shifts (left, right, up, down), reflections (across the X-axis and Y-axis), as well as vertical and horizontal stretches and compressions. Each problem presents a graph of a transformed function, and students must select the correct description of the transformation from multiple choices, enhancing their grasp of function manipulation and graphical interpretation.

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 Definition Worksheet

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

What transformation of f(x) does this graph show?

a $A LaTex expression showing f(x) = x to the power of 3 \\\text{Shift left: }5\\$

b $A LaTex expression showing f(x) = x to the power of 3 \\\text{Shift right: }5\\$

What transformation of f(x) does this graph show?

a $A LaTex expression showing f(x) = x to the power of 3 \\\text{Shift down: }4\\$

b $A LaTex expression showing f(x) = x to the power of 3 \\\text{Shift up: }4\\$

What transformation of f(x) does this graph show?

a $A LaTex expression showing f(x) = x to the power of 2 \\\text{Reflect in Y-Axis}\\$

b $A LaTex expression showing f(x) = x to the power of 2 \\\text{Reflect in X-Axis}\\$

What transformation of f(x) does this graph show?

a $A LaTex expression showing f(x) = x to the power of 2 \\\text{Reflect in X-Axis}\\$

b $A LaTex expression showing f(x) = x to the power of 2 \\\text{Reflect in Y-Axis}\\$

What transformation of f(x) does this graph show?

a $A LaTex expression showing f(x) = x to the power of 2 \\\text{Vertical compression: }2\\$

b $A LaTex expression showing f(x) = x to the power of 2 \\\text{Horizontal stretch: }2)\\$

c $A LaTex expression showing f(x) = x to the power of 2 \\\text{Vertical stretch: }2\\$

What transformation of f(x) does this graph show?

a $A LaTex expression showing f(x) = x\\\text{Shift right: }3\\$

b $A LaTex expression showing f(x) = x\\\text{Shift left: }3\\$

What transformation of f(x) does this graph show?

a $A LaTex expression showing f(x) = x\\\text{Shift right: }2\\$

b $A LaTex expression showing f(x) = x\\\text{Shift left: }2\\$

What transformation of f(x) does this graph show?

a $A LaTex expression showing f(x) = x to the power of 2 \\\text{Shift right: }3\\$

b $A LaTex expression showing f(x) = x to the power of 2 \\\text{Shift up: }3\\$

c $A LaTex expression showing f(x) = x to the power of 2 \\\text{Shift left: }3\\$