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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 4 — Mastery

Given the function $f(x) = x^{2}$ , what is the equation of the function after a vertical stretch by a factor of 3 and a downward shift of 2 units?

3x^{2} - 2

3(x^{2} - 2)

3x^{2} + 2

x^{2} + 2

If the function $g(x) = -2(x - 4)^{2} + 5$ represents a transformation of the parent function $y = x^{2}$ , what are the vertex coordinates of ?

What is the effect on the graph of the function $h(x) = (x + 1)^{2} - 3$ compared to the parent function $y = x^{2}$ ?

Consider the function $j(x) = - rac{1}{2}(x - 2)^{2} + 4$ . Which of the following describes its transformations relative to the parent function $y = x^{2}$ ?

Reflected over x-axis, vertical compression by 1/2, shifted right 2 units, and up 4 units

Reflected over x-axis, vertical stretch by 2, shifted left 2 units, and down 4 units

No transformations

Shifted left 2 units and down 4 units

The function $k(x) = 3|x + 2| - 1$ is a transformation of the parent function $y = |x|$ . What is the vertex of ?

If $m(x) = (x - 3)^{2} + 2$ represents a transformation of $y = x^{2}$ , which of the following describes the transformation?

For the function $p(x) = - rac{1}{3}(x + 4)^{2} + 6$ , what is the direction of the opening of the parabola?

Opens downwards

Opens upwards

Neither

Opens sideways

The function $q(x) = 2|x - 1| + 3$ represents a transformation of the parent function $y = |x|$ . What is the effect on the graph?

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