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MATH 112 Practice Test #2
Determine which two functions are inverses of each other.
Show mathematical justification for your answer.
Inverse
functions:__________________________
Find the inverse of the onetoone function.
______________________________________
Graph f as a solid line and f^{1} as a dashed line in the
same rectangular coordinate space. Use interval notation to give the domain
and range of f and f^{1}. Include a table of at least five values for f and f^{1}
below.
Write the standard form of the equation of the circle with the given center and
radius.
4) (3, 9);
1
__________________________________
Find the center and the radius of the circle.
5) (x  9)^{2} + (y + 8)^{2} = 25
Center:
_______________ Radius: ________________
Complete the square and write the equation in standard
form. Then give the center and radius of the circle.
6) x^{2} + y^{2} + 2x + 12y = 28
Center:____________
Radius:____________
Divide and express the result in standard form.
___________________________
For the given quadratic function , answer each of the
following questions.
8) f(x) = x^{2} + 4x  6
a.) Without graphing, find the vertex.
vertex:_____________
b.) Does the function have a minimum or maximum value? _________________ What is
that value? ___________
c.) What is the function's domain? domain:_____________
d.) What is the function's range? range:______________
Find the coordinates of the vertex for the parabola
defined by the given quadratic function.
9) f(x) = (x + 9)^{2}  8 vertex: ___________________
Use the the information you find in parts ad below to
sketch the graph of the quadratic function.
10) f(x) = x^{2}  2x  3
a.) What is the vertex of f(x)? ___________
b.) Write the equation of the axis of symmetry. ______________
c.) Find the xintercept(s), if any. _____________________
d.) Find the yintercept. _____________
Find the zeros of the polynomial function . State the multiplicity of each zero
and whether the graph crosses the x axis, or touches
the xaxis and turns around, at each intercept .
11) f(x) = x^{2}(x + 3)(x^{2}  1)
zeros  multiplicity  behavior of f(x) 
Use the Leading Coefficient Test to determine the end behavior of the polynomial
function.
12) f(x) = 5x^{3}  3x^{2}  2x + 3
__________________________________
Sketch the polynomial function by using the information
found in parts a c.
13) f(x) = x^{3} + 8x^{2}  x  8
a.) Determine the graph's end behavior.
b.) Find the xintercepts , the multiplicity , and the behavior of the graph at
each.
xintercept zeros 
multiplicity  behavior of f(x) 
c.) Find the yintercept.
Use the Intermediate Value Theorem to determine whether
the polynomial function has a real zero between the given integers.
Show mathematical justification for your answer and explain your findings.
14) f(x) = 7x^{3}  10x  2; between 2 and 1
Divide using long division. Determine q(x) and r(x).
q(x):__________________
r(x):___________________
Divide using synthetic division . Determine q(x) and r(x).
16) (x^{2} + 8x + 9) ÷ (x + 5)
q(x):__________________
r(x):___________________
Use the Remainder Theorem to find the indicated function
value.
17) f(x) = 3x^{4} + 10x^{3} + 3x^{2}  3x + 65; f(2)_______________________
Use the Rational Zero Theorem to list all possible
rational zeros for the given function.
18) f(x) = 7x^{4}  x^{2} + 2
____________________________________
Find a rational zero of the polynomial function and use it
to find all the zeros of the function.
19) f(x) = x^{3}  5x^{2} + 7x + 13
zeros:__________________________
Find an nth degree polynomial function with real
coefficients satisfying the given conditions.
20) n = 3;  6 and i are zeros; f(3) = 60
f(x) = _________________________________
Find the domain of the rational function. Write answer in
interval notation.
domain:_______________________
Use the graph of the rational function shown to complete
the statement.
22)
Find the vertical asymptotes, if any, of the graph of the
rational function.
Vertical asymptote(s):___________________
Find the horizontal asymptote, if any, of the graph of the
rational function.
Horizontal asymptote:__________________
Find the slant asymptote, if any, of the graph of the
rational function.
Slant asymptote:___________________
Graph the rational function by using the information in
parts a  e. Show work to the side and place answers underneath prompts.
a.) Find the vertical asymptote(s), if any.
b.) Find the horizontal asymptote, if any.
c.) Find the xintercept(s), if any.
d.) Find the yintercept.
e.) Make a list of additional points to be used in your graph.
f.) Graph the function using the information above.
Answer Key
Testname: MTH 112 BTZ PRACTICE TEST #2 (SECT. 1.8, 1.9, 2.1‐2.6) FA07
1) None
2) f^{1}(x) = x^{3}  2
3)
f domain = (0, ∞); range = (4, ∞)
f1 domain = (0, ∞); range = (4, ∞)
4) (x  3)^{2} + (y + 9)^{2} = 1
5) (9, 8), r = 5
6) (x + 1)^{2} + (x + 6)^{2} = 9
(1, 6), r = 3
8) (2, 2)
9) (9, 8)
10)
11) 0, touches the xaxis and turns
around;
3, crosses the xaxis;
1, crosses the xaxis;
1, crosses the xaxis
12) falls to the left and rises to the right
13)
14) f(2) = 38 and f(1) = 1; yes
17) 51
18) ± 1/7, ± 2/7, ± 1, ± 2
19) {1, 3 + 2i, 3  2i}
20) f(x) = 2x^{3} + 12x^{2} + 2x + 12
21) {xx ≠ 8, x ≠ 8}
22) +∞
23) x = 2
24) y = 3
25) y = x  13
26)
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