Algebra 2 Transformations of Functions Quiz: 10 Questions with Explanations

A Shifted right 3B Shifted left 3C Stretched by 3D Shifted up 3

Adding 3 to every output raises the graph by 3.

A Shifted right 5B Shifted left 5C Shifted up 5D Shifted down 5

The input must be 5 larger for the same output, so the graph moves right.

A The top-left panelB The bottom-right panel (reflected over the x-axis)C The top-right panelD The bottom-left panel

-f(x) flips the graph over the x-axis, so the V opens downward.

A \((-3, 1)\)B \((3, -1)\)C \((2, 1)\)D \((3, 1)\)

The vertex of |x| moves right 3 and up 1. The factor 2 does not move the vertex.

A \(f(x) = x^{3}\)B \(f(x) = x^{2} – 5\)C \(f(x) = x + 1\)D \(f(x) = x^{3} + x\)

f(-x) = (-x)² – 5 = x² – 5 = f(x).

A \(g(x) = \sqrt{x – 2} + 1\)B \(g(x) = \sqrt{x + 2} + 1\)C \(g(x) = \sqrt{x – 2} – 1\)D \(g(x) = \sqrt{x} + 3\)

The starting point moves right 2 and up 1.

A \(y \ge 5\)B \(y \ge 0\)C \(y \le 5\)D \(y \le 0\)

Since √x ≥ 0, -√x ≤ 0, and adding 5 gives g(x) ≤ 5.

A \((2, 6)\)B \((4, 4)\)C \((4, 8)\)D \((6, 6)\)

Subtracting 2 from the output lowers the point to (4, 4).

A 5B -1C 1D 3

x = 2 uses the second rule: 3 – 2 = 1.

A Reflection over the y-axisB Reflection over the x-axisC Shift leftD Vertical stretch by -1

Replacing x with -x flips the graph left-right, over the y-axis.