This algebra 1 transformations test answer key gives the full solution and the scoring guide for each of the 9 test questions on transformations, absolute value and piecewise functions.
Use this key to score the test out of 20 points. Each solution shows the work and the scoring rule. Give partial credit as described, and check that graphs show correct vertices, intercepts and circle types before awarding the graph point.
Algebra 1 Transformations Test Answer Key: questions 1–5
Question 1: Identify the shifts (2 points)
(a) \(g(x)=f(x)-5\): the graph shifts down 5 units; the vertex is \((0,-5)\).
(b) \(h(x)=f(x+6)\): the graph shifts left 6 units; the vertex is \((-6,0)\).
Scoring: 1 point each for the correct direction and distance. Reversing left and right earns 0 for part (b).
Question 2: Equation from a graph (2 points)
The vertex is \((-2,3)\), so \(h=-2\) and \(k=3\). \(g(x)=(x+2)^{2}+3\)
Check with \((0,7)\): \((0+2)^{2}+3=7\).
Scoring: 1 point for \(h=-2\) (written as \(x+2\)); 1 point for \(k=3\).
Question 3: Combine transformations (2 points)
Stretch by 3 and flip: \(-3|x|\). Shift right 2: \(-3|x-2|\). Shift up 1: \(-3|x-2|+1\).
\(g(x)=-3|x-2|+1\), vertex \((2,1)\).
Scoring: 1 point for the factor \(-3\) and the form \(a|x-h|+k\); 1 point for \(h=2\) and \(k=1\) (the vertex).
Question 4: Graph an absolute value function (3 points)
(a) \(h=-1\), \(k=4\): the vertex is \((-1,4)\).
(b) \(-|x+1|+4=0\) gives \(|x+1|=4\), so \(x=3\) or \(x=-5\): \((3,0)\) and \((-5,0)\).
(c) Plot the vertex, the intercepts and \((0,3)\), \((-2,3)\), then draw the two rays.
Scoring: 1 point each for (a), (b) and (c); in (c) the graph must open down with the correct vertex and intercepts.
Question 5: Evaluate a piecewise function (2 points)
\(f(-2)=2(-2)+3=-1\) (since \(-2 < 1\)).
\(f(1)=8-1^{2}=7\) (since \(1\ge 1\)).
\(f(3)=8-3^{2}=8-9=-1\). \(-1\), \(7\), \(-1\)
Scoring: 2 points for all three correct; 1 point for exactly two correct.
Algebra 1 Transformations Test Answer Key: questions 6–9
Question 6: Graph a piecewise function (3 points)
Left piece: \(f(-2)=4\), \(f(0)=2\); at \(x=1\) the rule gives 1, an open circle at \((1,1)\).
Right piece: \(f(1)=2-3=-1\), a closed circle at \((1,-1)\); \(f(2)=1\), \(f(3)=3\).
Scoring: 1 point for the correct left piece; 1 point for the correct right piece; 1 point for the correct open and closed circles at \(x=1\).
Question 7: Read a step function (2 points)
(a) At \(x=2\) the closed circle is at height 6. \(\$6\)
(b) 2.5 pounds is between 2 and 3, where the height is 8. \(\$8\)
Scoring: 1 point for each correct cost. Answering \(\$7\) for part (b) by connecting the steps earns 0.
Question 8: Tolerance of rods (2 points)
(a) \(|11.7-12|=|-0.3|=0.3>0.25\). Not acceptable.
(b) \(-0.25\le x-12\le 0.25\), so \(11.75\le x\le 12.25\).
Scoring: 1 point for (a) with the value 0.3 compared with 0.25; 1 point for (b).
Question 9: Inside or outside (2 points)
\(y=(x+3)^{2}\) shifts \(y=x^{2}\) left 3: vertex \((-3,0)\); at \(x=0\), \(y=9\), so the y-intercept is \((0,9)\).
\(y=x^{2}+3\) shifts \(y=x^{2}\) up 3: vertex \((0,3)\); at \(x=0\), \(y=3\), so the y-intercept is \((0,3)\).
The vertices and y-intercepts differ, so the graphs are different.
Scoring: 1 point for the two correct vertices; 1 point for the two correct y-intercepts.
Scoring summary
20 points: add the points of every question of this algebra 1 transformations test answer key.
How to use this algebra 1 transformations test answer key
Use this algebra 1 transformations test answer key to score the test fairly and to see which skills need more practice.
See every chapter on the Algebra 1 math page.