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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?

Shift right by 1 unit.

Shift left by 1 unit.

Shift up by 4 units.

Shift down by 2 units.

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

Shift right by 2 units.

Shift left by 2 units.

Shift up by 2 units.

Shift down by 2 units.

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

Shift left by 2 units.

Shift right by 2 units.

Stretch vertically by a factor of 3.

Shift down by 2 units.

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.

Horizontal stretch by a factor of 2.

Horizontal compression by a factor of 2.

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

Reflection over the y-axis.

Reflection over the x-axis.

Shift right by 1 unit.

Shift left by 1 unit.

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 $f(x) = x^{3}$ ?

Shift down by 1 unit.

Shift up by 1 unit.

Shift left by 1 unit.

Shift right by 1 unit.

For the function $f(x) = -x^{2}$ , what is the transformation of $g(x) = -f(x - 2)$ ?

Shift right by 2 units and reflect over the x-axis.

Shift left by 2 units and reflect over the x-axis.

Shift up by 2 units and reflect over the y-axis.

Shift down by 2 units and reflect over the y-axis.

10.

What is the effect of the transformation $h(x) = f(x) + 5$ on $f(x)$ ?

Shift up by 5 units.

Shift down by 5 units.

Shift left by 5 units.

Shift right by 5 units.

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