Transformations of Functions: Algebra 2 Math Test – PDF Download

Question 1: Shifts of absolute value (2 points)

Let \(g(x)=|x+3|-5\) and \(f(x)=|x|\).

1. Describe how the graph of \(g\) differs from the graph of \(f\). (1 point)
2. Give the vertex of \(g\). (1 point)

Question 2: Transform points (2 points)

The graph of \(f\) contains the points \((-4,2)\), \((0,-3)\) and \((6,5)\). Give three points on each graph.

1. \(g(x)=f(x+3)\) (1 point)
2. \(h(x)=2f(x)\) (1 point)

Question 3: Write an equation (2 points)

The graph of \(f(x)=x^{2}\) is reflected over the x-axis, then shifted right 2 and up 7 to form \(g\).

1. Write an equation for \(g(x)\). (1 point)
2. Find \(g(5)\). (1 point)

Question 4: Even and odd (3 points)

Determine whether each function is even, odd or neither. Show the work.

1. \(f(x)=2x^{4}-x^{2}\) (1 point)
2. \(g(x)=x^{3}-5x\) (1 point)
3. \(h(x)=x^{2}+3x\) (1 point)

Question 5: Graph a square root (3 points)

Graph \(y=\sqrt{x+1}-2\) and state its domain and range.

Question 6: Cube root from a graph (2 points)

Write an equation of the form \(y=\sqrt[3]{x-h}+k\) for the graph.

Question 7: Stretch and reflect (2 points)

The graph of \(g(x)=-\frac{1}{2}|x|+4\) is a transformation of \(f(x)=|x|\).

1. Describe every transformation. (1 point)
2. Find \(g(6)\). (1 point)

Question 8: Exponential graph (2 points)

The graph of \(g(x)=2^{x}-4\) is shown.

1. State the horizontal asymptote. (1 point)
2. State the x-intercept. (1 point)

Question 9: Skid speed (2 points)

A car’s speed in miles per hour is \(s(d)=\sqrt{24d}\), where \(d\) is the skid length in feet.

1. Find the speed for a 24-foot skid. (1 point)
2. Find the skid length for a speed of 36 mph. (1 point)

⬇ Download the Algebra 2 Transformations of Functions test (PDF, 94 KB)

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