Transformations, Absolute Value and Piecewise Functions: Algebra 1 Math Test – PDF Download

Question 1: Identify the shifts (2 points)

Let \(f(x)=|x|\). Describe how the graph of each function compares with the graph of \(f\).

1. \(g(x)=|x|-5\) (1 point)
2. \(h(x)=|x+6|\) (1 point)

Question 2: Equation from a graph (2 points)

The graph of \(g\) is a shifted copy of \(f(x)=x^{2}\). Write \(g(x)\) in the form \(g(x)=(x-h)^{2}+k\).

Question 3: Combine transformations (2 points)

The graph of \(f(x)=|x|\) is stretched vertically by a factor of 3, flipped over the x-axis, shifted 2 units right and then shifted 1 unit up. Write the equation of the new function \(g\) and state its vertex.

Question 4: Graph an absolute value function (3 points)

Consider \(g(x)=-|x+1|+4\).

1. Find the vertex. (1 point)
2. Find the x-intercepts. (1 point)
3. Graph \(g\) on the grid. (1 point)

Question 5: Evaluate a piecewise function (2 points)

Let \(f(x)=2x+3\) when \(x < 1\), and \(f(x)=8-x^{2}\) when \(x\ge 1\). Find \(f(-2)\), \(f(1)\) and \(f(3)\).

Question 6: Graph a piecewise function (3 points)

Graph \(f(x)=-x+2\) when \(x < 1\), and \(f(x)=2x-3\) when \(x\ge 1\), on the grid. Use open and closed circles correctly.

Question 7: Read a step function (2 points)

The graph shows the cost of shipping a package. Find the cost of (a) a 2-pound package and (b) a 2.5-pound package. (1 point each)

Question 8: Tolerance of rods (2 points)

A factory cuts rods to \(x\) inches. A rod is acceptable when \(|x-12|\le 0.25\).

1. Is a rod that is 11.7 inches long acceptable? Show why. (1 point)
2. Write all acceptable lengths as a compound inequality. (1 point)

Question 9: Inside or outside (2 points)

Maya says the graphs of \(y=(x+3)^{2}\) and \(y=x^{2}+3\) are the same. Show that she is wrong by giving the vertex of each graph and the y-intercept of each graph.

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