Math-180-Exam #1
Practice Exam
Name___________________________________
Date: _________________________
Instructions: Show all work neatly. Answers without support will receive no credit. Your answers will be evaluated on
the correctness, completeness and use of mathematical concepts we have covered.
Graph the equation.
1) y = x3 - 5
1)
Graph the given functions on the same rectangular coordinate system. Describe how the graph of g is related to the graph
of f.
2) f(x) = 2x2, g(x) = 2x2 - 3
2)
1
Use the graph to determine the function's domain and range.
3)
3)
Determine whether the given function is even, odd, or neither.
4) f(x) = x3 - x2
4)
Use possible symmetry to determine whether the graph is the graph of an even function, an odd function, or a function
that is neither even nor odd.
5)
5)
Graph the function.
6) f(x) = -x + 3
2x - 3
if x < 2
if x 2
6)
2
Find and simplify the difference quotient
f(x + h) - f(x)
, h 0 for the given function.
h
7) f(x) = 2x2
7)
Use the given conditions to write an equation for the line in slope-intercept form.
8) Passing through (2, 5) and (1, 8)
8)
Determine the slope and the y-intercept of the graph of the equation.
9) -x + 6y - 12 = 0
9)
Graph the equation.
10) 2x + 3y - 10 = 0
10)
Find the domain of the function.
1
11) f(x) =
x+1
12) f(x) =
11)
1
4
+
x-2 x+8
12)
Use the given conditions to write an equation for the line in the indicated form.
13) Passing through (2, 2) and perpendicular to the line whose equation is y = 4x + 7;
point-slope form
For the given functions f and g , find the indicated composition.
x-4
,
g(x) = 6x + 4
14) f(x) =
6
13)
14)
(g f)(x)
Find the distance between the pair of points.
15) (3 3, 2) and (7 3, 3)
15)
Write the standard form of the equation of the circle with the given center and radius.
16) (-9, 8); 3
16)
3
Begin by graphing the standard quadratic function f(x) = x 2 . Then use transformations of this graph to graph the given
function.
17) h(x) = (x + 6)2 - 3
17)
Graph the equation.
18) (x - 1)2 + (y - 5)2 = 4
18)
Find the distance between the pair of points.
19) (5, 5) and (1, -7)
19)
Complete the square and write the equation in standard form. Then give the center and radius of the circle.
20) x2 + y2 + 6x - 2y + 10 = 36
20)
Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the
x-axis or touches the x-axis and turns around, at each zero.
21) f(x) = 5(x + 2)(x + 1)3
21)
Divide using synthetic division.
5x3 - 25x2 - 29x - 6
22)
x-6
22)
Use synthetic division and the Remainder Theorem to find the indicated function value.
23) f(x) = x 4 - 5x3 - 8x2 - 4x + 9; f(4)
4
23)
Use the Rational Zero Theorem to list all possible rational zeros for the given function.
24) f(x) = x 5 - 5x2 + 5x + 21
25) f(x) = 6x4 + 4x3 - 2x2 + 2
24)
25)
Find a rational zero of the polynomial function and use it to find all the zeros of the function.
26) f(x) = 3x3 - 17x2 + 18x + 8
26)
Use Descartes's Rule of Signs to determine the possible number of positive and negative real zeros for the given function.
27) f(x) = 3x3 - 3x2 + x + 3
27)
Find the domain of the rational function.
x+2
28) g(x) =
x2 - 64
28)
Use the graph of the rational function shown to complete the statement.
29)
As x -1 + , f(x)
29)
?
Find the vertical asymptotes, if any, of the graph of the rational function.
x-2
30) g(x) =
x(x + 3)
Find the horizontal asymptote, if any, of the graph of the rational function.
8x2
31) g(x) =
2x2 + 1
5
30)
31)
Answer Key
Testname: MATH-180-E1-PRACTICE
1)
2) g shifts the graph of f vertically down 3 units
3) domain: [0, )
range: [-1, )
4) Neither
5) Even
6)
7) 2(2x+h)
8) y = - 3x + 11
1
9) m = ; (0, 2)
6
6
Answer Key
Testname: MATH-180-E1-PRACTICE
10)
11) (- , -1)
12) (- , -8)
(-1, )
(-8, 2) (2, )
1
13) y - 2 = - (x - 2)
4
14) x
15) 7
16) (x + 9)2 + (y - 8)2 = 9
17)
18)
Domain = (-1, 3), Range = (3, 7)
19) 4 10
20) (x + 3)2 + (y - 1)2 = 36
(-3, 1), r = 6
7
Answer Key
Testname: MATH-180-E1-PRACTICE
21) -2, multiplicity 1, crosses x-axis; -1, multiplicity 3, crosses x-axis
22) 5x2 + 5x + 1
23) -199
24) ± 1, ± 7, ± 3, ± 21
1
1
1
2
25) ± , ± , ± , ± , ± 1, ± 2
6
3
2
3
26) -
1
, 2, 4
3
27) 2 or 0 positive zeros, 1 negative zero
28) {x|x -8, x 8}
29) +
30) x = 0 and x = -3
31) y = 4
8