Honors Math 2Name:
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Final Exam Review – Algebra Problems
Function Concept (Chapter 4A, 4B, 4D)
1.a.Which of the following recursive functions best fits the table below?
Input, n / Output, a(n)0 / 2
1 / -1
2 / -7
3 / -19
4 / -43
5
i.
ii.
iii.
iv.
b.Fill in the value for a(5) in the table using the definition you chose.
x / f(x) / /0 / 3 / 3 / 2
1
2 / 7
3 / 2
4
5 / 32
2.a.Complete the difference table for the quadratic function f(x).
b.Find a closed-form function that agrees with the table.
c.Find a recursive function that agrees with the table.
3.For each function, find the domain and range.
a.b.
c.d.
e.f.
4.Consider the functions and . Find each value or formula.
a.b.
c.d.
5.Below are the graphs of three functions. Which functions are one-to-one, if any?
6.The graph shows a piecewise-defined function.
a.Write a function for this graph.
b.Write the piecewise definition for the inverse
of this function.
c.Carefully sketch the graph of the inverse of
this function.
7.Find the formula for and state the domain of the function and its inverse.
8.Sketch each of the basic graphs below. You should be able to do this from memory.
9.Sketch each of the transformations of the basic graphs below. Describe how the basic graph has been transformed.
a./ b.
/ c.
/ d.
10.Let .
a.Show that f is an even function by showing that .
b.Show that f is an even function by using the graph of f.
11. Let .
a.Explain why the graph of f resembles the graph of near the origin.
b.Explain why the graph of f resembles the graph of far away from the origin.
c.Find the x-intercepts of the graph of f.
d.Find the x-intercepts of the graph of .
e.Sketch the graph of . How are the graphs of f and g related?
Exponents and Radicals (Chapter 1)
12.Here is an input-output table for the function .
Simplify each square root.
a.b.
c.d.
e.f.What is the pattern?
13.Draw a diagram of the sets of Z, Q, and R. Then place each number in the diagram.
a.b.c.d.
e.f.g.h.
14.Decide whether each expression equals . Explain.
15.a.What number is defined to be ?
b.What is ? Use a law of exponents.
16.Show that .
Polynomial and Quadratic Functions (Chapters 2, 3A, 3B)
17.a.What values of m make a perfect square trinomial?
b.What values of n make a perfect square trinomial?
18.Find a value of p such that has the following solutions.
a.two real-number solution
b.one real-number solution
c.no real-number solutions
19.Find a quadratic equation for the given roots.
a.12 and 4
b. and
20.Solve the following quadratic equations. Use the most efficient method.
a.b.c.
d.e.f.
g.h.i.
21.Sketch the graph of and find the vertex and line of symmetry.
22.A quadratic function has zeros 3 and 9. It passes through point (6,11). What is the vertex of the graph?
Analytic Geometry, i.e. Conic Sections (Honors Appendix F and extra material)
23.Consider an ellipse with foci and . The locus definition of the ellipse is the set of points P with .
a.Find the two values of b so that is on the ellipse.
b.Find the two values of a so that is on the ellipse.
c.Is the point (2,5) on the ellipse? Explain how you know.
24.a.Find c if is on the parabola with focus (2,0) and directrix with equation .
b.Find b if is on the parabola with focus (2,0) and directrix with equation .
c.Find an equation of the parabola with focus (2,0) and directrix with equation .
25.a.Put the equation into standard form. Identify the type of conic section that this equation represents.
b.Sketch the graph of the equation. Identify the coordinates of the center, vertices, co-vertices, and foci, and write the equations of the asymptotes, if they exist.
Algebra Answers
Function Concept (Chapter 4A, 4B, 4D)
1.a. ii.b. –91
2.b.closed-form:
c.recursive:
3.a.domain: R; range: b.domain: ; range:
c.domain: ; range: d.domain: R; range: all pts. satisfying
e.domain: ; range: Rf.domain: ; range:
4.a.33b.c.d.
5.II
6.a.b.
7.
8.Check the basic graphs by graphing on your calculator.
9.Check the transformed graphs by graphing on your calculator.
a.Translate left 4 and up 2.
b.Reflect over the y-axis and vertically compress by a factor of 2.
c.Translate right 5 units and reflect over the x-axis.
d.Horizontally compress by a factor of 2. Also can be vertical compression by 2 ()
10.a.
b.The graph of has symmetry across the y-axis. This means that if
you replace each point with the point you get the same graph.
11.a.The closer to the origin, the more negligible the term becomes.
The x term has more of an effect on the graph.
b.The farther away from the origin, the larger the term becomes. It therefore has a more significant effect on the graph than the x term.
c.(1,0) and (0,0)d. (1,0) and (2,0)
e.The graph of g is a translation of the graph of f two units to the right.
Exponents and Radicals (Chapter 1)
12.a.b.c.d.e.
f.For any positive number x, .
13.
14.a.Yes; add the exponents.
b.Yes; add the exponents.
c.No; you cannot add the exponents.
d.No;subtract the exponents to get .
e.Yes;subtract the exponents.
f.No;the bases are not equal, so there is no reasonable result.
g.Yes;multiply the exponents in the numerator and then subtract the exponents.
h.Yes;multiply the exponents in the numerator and denominator by the outer exponent. Then subtract the exponents.
15.a.2b.
16.
Polynomial and Quadratic Functions (Chapters 2, 3A, 3B)
17.a.b.25
18.a.b.c.
19.a.b.
20.a.b.c.
d.e.f.
g.h.i.
21.
22.
Analytic Geometry, i.e. Conic Sections (Honors Appendix F and extra material)
23.a.8 and 8
b.10 and 10
c.No;
24.a.
b.
c.
25.a.; hyperbola
b.Center (2,5), Vertices (2,5) and (6,5),
Co-vertices (2,2) and (2,8), Foci (-3,5) and (7,5),
Asymptotes