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SAT Math - Graphing and Transforming Functions - Function Transformations | Worksheet

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Function Transformations

This worksheet covers Function Transformations, which is part of the Graphing and Transforming Functions module in the SAT Math course. Practice problems are designed to strengthen key concepts and build confidence.

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Function Transformations

Graphing and Transforming Functions • SAT Math

Set 1 — Foundation

What is the effect of the transformation $f(x) = x^{2} + 3$ compared to $f(x) = x^{2}$ ?

The graph shifts upward by 3 units.

The graph shifts downward by 3 units.

The graph shifts left by 3 units.

The graph shifts right by 3 units.

If $g(x) = -2x + 4$ , what transformation does $h(x) = -2(x - 1) + 4$ represent?

What is the transformation of the function $f(x) = |x|$ to $g(x) = |x - 2|$ ?

If $f(x) = 3x^{2}$ , what is the effect of the transformation $g(x) = 3(x + 2)^{2}$ ?

What is the transformation for $h(x) = 2f(x)$ compared to $f(x)$ ?

Vertical stretch by a factor of 2.

Vertical compression by a factor of 2.

Given $f(x) = x^{2}$ , what does the function $g(x) = f(-x)$ represent?

If $f(x) = rac{1}{x}$ , what is the transformation for $g(x) = rac{1}{x + 3}$ ?

Shift left by 3 units.

Shift right by 3 units.

Shift up by 3 units.

Shift down by 3 units.

What effect does the transformation $f(x) = x^{3} - 1$ have on the graph of $f(x) = x^{3}$ ?

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