Regents Exam Questions CC.A.REI.11: Other Systems
Page 1
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Name: __________________________________
CC.A.REI.11: Explain why the x-coordinates of the points where the graphs of the
equations y=f(x) and y=g(x) intersect are the solutions of the equation f(x)=g(x);
find the solutions approximately, e.g., using technology to graph the functions,
make tables of values, or find successive approximations. Include cases where f(x)
and/or g(x) are linear, polynomial, rational, absolute value, exponential, and
logarithmic functions.
1 The graphs of the functions
functions is true?
1) The solution to
is 3.
2) The solution to
is 1.
3) The graphs intersect when
.
4) The graphs intersect when
.
and
are drawn. Which statement about these
2 Two functions,
and
, are graphed on the same set of axes. Which statement is true
about the solution to the system of equations?
1)
is the solution to the system because it
satisfies the equation
.
2)
is the solution to the system because it
satisfies the equation
.
3)
is the solution to the system because it
satisfies both equations.
4)
,
, and
are the solutions to the
system of equations because they all satisfy
at least one of the equations.
3 Given the functions
and
, which value of x makes
?
1)
2) 2
3) 3
4)
4 What is the total number of points of intersection for the graphs of the equations
1) 1
2) 2
3) 3
4) 0
and
?
Regents Exam Questions CC.A.REI.11: Other Systems
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Name: __________________________________
5 What is one solution of the accompanying system of equations?
1)
2)
3)
4)
6 The graphs of the equations
1)
2)
3)
4)
and
intersect in Quadrant I for which values of a?
7 The flight paths of two Thunderbird jets are plotted on a Cartesian coordinate plane, and the equations of
the jets' flight paths are represented by
and
. The best approximation of the intersection
of the flight paths is
1)
2)
3)
4)
8 On the accompanying grid, sketch the graphs of
and
Identify and state the coordinates of all points of intersection.
over the interval
.
Regents Exam Questions CC.A.REI.11: Other Systems
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Name: __________________________________
9 On the accompanying grid, solve the following system of equations graphically:
10 On the set of axes below, graph
How many values of x satisfy the equation
graphs.
? Explain your answer, using evidence from your
Regents Exam Questions CC.A.REI.11: Other Systems
www.jmap.org
1 ANS: 2
REF: 061622ai
2 ANS: 3
3 ANS: 1
REF: 011518ai
REF: 011617ai
4 ANS: 1
.
REF: 080611b
5 ANS: 3
REF: 060706b
6 ANS: 4
The function
passes through Quadrant I only if
The function
axis at
and continues through Quadrant I with a positive slope. If
equations intersect at (0,1), which is not in Quadrant I. Therefore,
intersects the ythe graphs of the
Regents Exam Questions CC.A.REI.11: Other Systems
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REF: 060519b
7 ANS: 1
REF: 080705b
8 ANS:
REF: 010628b
9 ANS:
REF: 010527b
10 ANS:
1, because the graphs only intersect once.
REF: 061636ai