This algebra 2 function interpretation quiz asks 10 multiple-choice questions on interpreting and comparing functions, and each answer comes with a short explanation.
Ten multiple-choice questions check key features of graphs, domain in context, average rate of change, completing the square, factored form and comparing functions. Exactly one option is correct in each question, and the explanation points out the usual mistake.
🎯 Interpreting and Comparing Functions – Algebra 2 math quiz
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Question 1
The graph shows a parabola with vertex \((2,-1)\). On which interval is the function decreasing?
A\((2,\infty)\)
B\((1,3)\)
C\((-\infty,2)\)
D\((-\infty,1)\)
Question 2
A rectangular pen has area \(A(w)=w(30-w)\) square feet, where \(w\) is the width in feet. What is the domain in this context?
Aall real numbers
B\(0 < w < 30\)
C\(w\ge 0\)
D\(0\le w\le 15\)
Question 3
Find the average rate of change of \(f(x)=x^{2}+1\) on \([1,3]\).
A8
B5
C2
D4
Question 4
The graph of an exponential function passes through \((1,2)\) and \((3,8)\). What is its average rate of change from \(x=1\) to \(x=3\)?
A3
B6
C4
D5
Question 5
Complete the square: \(x^{2}+10x+7\) equals which expression?
A\((x+5)^{2}+7\)
B\((x+5)^{2}-18\)
C\((x+10)^{2}-93\)
D\((x+5)^{2}-25\)
Question 6
The function \(f(x)=(x-4)(x+2)\) is in factored form. Which feature does this form show directly?
AThe vertex (1, −9)
BThe y-intercept −8
CThe maximum value
DThe zeros 4 and −2
Question 7
What are the minimum value and its location for \(f(x)=x^{2}-6x+5\)?
A\(-4\) at \(x=-3\)
B\(4\) at \(x=3\)
C\(-4\) at \(x=3\)
D\(-3\) at \(x=-4\)
Question 8
The line graph of \(f\) passes through \((0,3)\) and \((2,7)\). Let \(g(x)=3^{x}\). Which function has the greater average rate of change on \([0,2]\)?
A\(f\) (rate 2 versus 1)
BThey are equal
C\(g\) (rate 4 versus 2)
DCannot be determined
Question 9
A club’s profit is \(P(x)=-x^{2}+10x-16\) dollars when tickets cost \(x\) dollars. What is the greatest possible profit?
A$9
B$5
C$25
D−$16
Question 10
The tide depth \(d(t)=6+4\sin\left(\frac{\pi t}{6}\right)\) is graphed below. What is its period?
A6 hours
B24 hours
C4 hours
D12 hours
🎉 Quiz complete!
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How does this quiz work?
Read each question, choose one answer among A, B, C and D, then check it: a short explanation appears after every answer. Your score out of 10 is shown at the end, and you can restart the quiz as often as you like.
What should you review before the quiz?
Reread the key facts of the lesson and the worked example. If a question is hard, go back to the matching part of the lesson, then try the quiz again. Write your work on scrap paper: most mistakes come from skipping a step, not from the idea itself.
Remember:
Standards F-IF.B.4, F-IF.B.5, F-IF.B.6, F-IF.C.8a and F-IF.C.9 on interpreting and comparing functions.
The domain of a model is limited by the context, such as time in the air or whole numbers of tickets.
Average rate of change on \([a,b]\) is \(\frac{f(b)-f(a)}{b-a}\), the slope of a secant line.
Factored form \(a(x-r)(x-s)\) shows zeros; vertex form \(a(x-h)^{2}+k\) shows the extreme value \(k\).
Compare two functions by finding the same feature (intercept, maximum, rate of change) from each representation.
How to use this algebra 2 function interpretation quiz
Retake this algebra 2 function interpretation quiz until every answer is right, then move on to the worksheet and the test.
