Interpreting and Comparing Functions: Algebra 2 Math Test – PDF Download

Question 1: Key features of a cubic (3 points)

The graph shows \(f(x)=x^{3}-3x\).

1. Find the zeros of \(f\). (1 point)
2. State the intervals on which \(f\) is increasing. (1 point)
3. Find the average rate of change of \(f\) on \([1,2]\). (1 point)

Question 2: Domain and maximum in context (2 points)

A rancher uses 60 feet of fence along a barn wall to enclose a rectangular pen on three sides. If the sides perpendicular to the barn have length \(w\) feet, the area is \(A(w)=w(60-2w)\) square feet.

1. State the domain of \(A\) in this context. (1 point)
2. Find the greatest possible area and the value of \(w\) that gives it. (1 point)

Question 3: Average rate of change (3 points)

The total cost \(C(n)\) of printing \(n\) team posters is given in the table.

1. Find the average rate of change of \(f(x)=x^{2}-4x\) on \([1,5]\). (1 point)
2. Find the average rate of change of \(C\) on \([10,30]\). (1 point)
3. Interpret your answer to part (b) in context. (1 point)

Question 4: Complete the square (3 points)

Let \(f(x)=x^{2}-8x+3\).

1. Rewrite \(f\) in vertex form by completing the square. (2 points)
2. State the minimum value of \(f\) and the \(x\)-value where it occurs. (1 point)

Question 5: Factored form of a quadratic (2 points)

Let \(g(x)=2x^{2}-2x-12\).

1. Factor \(g\) and find its zeros. (1 point)
2. Find the minimum value of \(g\). (1 point)

Question 6: Exponential features (2 points)

The graph shows \(f(x)=3^{x}-9\).

1. Find the y-intercept of \(f\). (1 point)
2. Write the equation of the horizontal asymptote. (1 point)

Question 7: Compare two functions (3 points)

Function \(f\) is \(f(x)=-(x-2)^{2}+9\). Function \(g\) is a quadratic with the values in the table.

1. Which function has the greater maximum value? Give both maximums. (1 point)
2. Which function has the greater y-intercept? Give both. (1 point)
3. Which function has the greater average rate of change on \([0,2]\)? Give both rates. (1 point)

Question 8: Periodic function (2 points)

The depth of water at a dock is \(d(t)=6+4\sin(\frac{\pi t}{6})\) feet, where \(t\) is the number of hours after 6:00 a.m.

1. State the period, the maximum depth and the minimum depth. (1 point)
2. Find the average rate of change on \([0,3]\) with units. (1 point)

⬇ Download the Algebra 2 Interpreting and Comparing Functions test (PDF, 99 KB)

See every chapter on the Algebra 2 math page.