Ten multiple-choice questions check whether you can find intercepts, read increasing and decreasing intervals, describe end behavior, compute an average rate of change and compare functions. Pick one answer for each question, then read the explanation.
Algebra 1Common Core: F-IF.B.4 · F-IF.B.6 · F-IF.C.9
🎯 Key Features of Graphs and Rate of Change – Algebra 1 math quiz
Question 1
What are the \(x\)-intercepts of \(f(x)=x^{2}-16\)?
A
\(x=16\) and \(x=-16\)
B
\(x=-4\) and \(x=4\)
C
\(x=4\) only
D
\(x=-16\) only
Question 2
What is the \(y\)-intercept of the function graphed?The graph of a function \(f\).
A
\(1\)
B
\(3\)
C
\(-3\)
D
\(2\)
Question 3
On which interval is the function decreasing?A graph made of three line segments.
A
\(-4 < x < -1\)
B
\(2 < x < 5\)
C
\(-1 < x < 2\)
D
\(-2 < x < 3\)
Question 4
What is the relative maximum of the function in the same graph?A graph made of three line segments.
A
The value \(-1\), at \(x=2\)
B
The value 3, at \(x=5\)
C
The value \(-1\), at \(x=3\)
D
The value 3, at \(x=-1\)
Question 5
What is the end behavior of \(f(x)=-x^{2}+3\) as \(x\) gets very large?
A
The outputs decrease without bound
B
The outputs increase without bound
C
The outputs approach 3
D
The outputs approach 0
Question 6
What is the average rate of change of \(f(x)=x^{2}-3x\) from \(x=2\) to \(x=5\)?
A
\(12\)
B
\(8\)
C
\(6\)
D
\(4\)
Question 7
The table shows miles driven. What is the average speed from \(t=2\) to \(t=6\) hours?Distance driven over time.
A
30 miles per hour
B
33 miles per hour
C
60 miles per hour
D
40 miles per hour
Question 8
Function \(f\) is \(f(x)=5x+2\). Function \(g\) is graphed. Which statement is true?The graph of a function \(g\).
A
Function \(f\) has the greater rate of change and the greater \(y\)-intercept
B
Function \(g\) has the greater rate of change, and \(f\) has the greater \(y\)-intercept
C
Function \(f\) has the greater rate of change, and \(g\) has the greater \(y\)-intercept
D
Function \(g\) has the greater rate of change and the greater \(y\)-intercept
Question 9
A tank holds \(V(t)=90-6t\) gallons after \(t\) minutes. What does the \(t\)-intercept \((15,0)\) mean?
A
The tank started with 15 gallons
B
The tank is empty after 15 minutes
C
The tank loses 15 gallons each minute
D
The tank holds 90 gallons after 15 minutes
Question 10
A parabola has \(x\)-intercepts at \(x=-1\) and \(x=7\). What is its axis of symmetry?
A
\(x=6\)
B
\(x=3\)
C
\(x=4\)
D
\(x=-3\)
🎉 Quiz complete!
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Remember:
- The x-intercepts are the inputs where f(x) = 0; the y-intercept is f(0).
- Increasing means the graph rises from left to right; decreasing means it falls.
- A relative maximum or minimum is a turning point, higher or lower than nearby points.
- Average rate of change = (f(b) – f(a)) / (b – a), with units.
- To compare functions, compare the same feature, such as rate or intercept.
See every chapter on the Algebra 1 math page.