Precalculus Transformations of Graphs Test Solutions and Scoring (PDF)

Left 2, reflect over the \(x\)-axis, up 4.

Left 2, reflect over the x-axis, up 4

Scoring: 1 point for the horizontal shift, 1 point for the reflection and vertical shift.

(a) \((5,-1)\). (b) \(x\) stays 4 and \(y=-2(-3)=6\): \((4,6)\).

(a) \((5,-1)\); (b) \((4,6)\)

Scoring: 1 point for each point.

Shift: \(\sqrt{x+4}\). Reflect: \(-\sqrt{x+4}\). Outputs are at most 0.

\(y=-\sqrt{x+4}\); range \((-\infty,0]\)

Scoring: 1 point for the equation, 1 point for the range.

(a) \(f(-x)=-x^{3}+5x=-f(x)\): odd. (b) \(g(-x)=x^{2}+1=g(x)\): even.

(a) odd; (b) even

Scoring: 1 point each, with the test shown.

(a) Vertex \((1,-3)\): \(y=|x-1|-3\). (b) The minimum is \(-3\), so the range is \([-3,\infty)\). (c) \(|x-1|=3\) gives \(x=4\) or \(x=-2\).

\(y=|x-1|-3\); \([-3,\infty)\); \(x=-2,\ 4\)

Scoring: 1 point for each part.

Double each output and subtract 1: \(2(4)-1=7\), \(2(1)-1=1\), \(2(0)-1=-1\).

7, 1, -1, 1

Scoring: 1 point for each pair of correct values (2 points total).

Right 2, vertical stretch 3, up 1. At \(x=11\): \(3\sqrt{9}+1=10\).

Value \(10\)

Scoring: 1 point for the description, 1 point for the value.

(a) \(8\) ft. (b) \(-0.5(4)+8=6\) ft. (c) \((x-4)^{2}=16\), so \(x=8\).

\(8\) ft; \(6\) ft; \(x=8\) ft

Scoring: 1 point for each part.

Shift: \((x-3)^{2}\). Stretch: \(2(x-3)^{2}\). Reflect: \(-2(x-3)^{2}\).

\(y=-2(x-3)^{2}\)

Scoring: 1 point for the shift and stretch, 1 point for the reflection.