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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 $g(x)$ ?

(4, 5)

(5, 4)

(2, -2)

(0, -2)

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

Shifted left 1 unit and down 3 units

Shifted right 1 unit and up 3 units

Reflected over the x-axis

Stretched vertically by a factor of 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 $k(x)$ ?

(-2, -1)

(2, 1)

(0, 1)

(-1, 3)

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

Shifted right 3 units and up 2 units

Shifted left 3 units and down 2 units

Reflected over x-axis

Stretched vertically by a factor of 2

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?

Vertical stretch by a factor of 2, shifted right 1 unit and up 3 units

Vertical compression by a factor of 2

Shifted left 1 unit and down 3 units

Reflected over the x-axis

If the function $r(x) = 5 - (x + 3)^{2}$ is transformed from the parent function $y = x^{2}$ , what are the properties of this transformation?

Reflected over x-axis, shifted left 3 units, and up 5 units

Shifted right 3 units and down 5 units

Stretched vertically by a factor of 5

None of the above

10.

Which transformation is applied to the function $s(x) = rac{1}{4}(x - 5)^{2} + 2$ compared to the parent function $y = x^{2}$ ?

Vertical compression by a factor of 4, shifted right 5 units and up 2 units

Vertical stretch by a factor of 4

Shifted left 5 units

Reflected over the x-axis

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