Review
Test 2
Math 1314
Name___________________________________
Write an equation of the line satisfying the given
conditions. Write the answer in standard form.
2
1) The line has a slope of - and contains
7
the point (3, 1).
Use the point-slope formula to write an equation
of the line that passes through the given points.
Write the answer in slope-intercept form (if
possible).
2) (3, 2) and (-3, -3)
Write an equation of the line satisfying the given
conditions. Write the answer in slope-intercept
form.
3) The line passes through (-6, 9) and
(-6, -15).
Sketch the graph using transformations of a
parent function (without a table of values).
4) The line passes through (2, 11) and
(11, 11).
6) r(x) = x + 4
From memory match each equation with its graph.
5)
f(x) = x
g(x) =
1
x
Write an equation of the line satisfying the given
conditions. Write the answer in standard form
with no fractional coefficients.
7) Passes through (-5, -1) and is parallel to
the line defined by 3x - 5y = 9
h(x) = x3
I II III
Sketch the graph using transformations of a
parent function (without a table of values).
8) a(x) = (x - 1)2
Use transformations to graph the given function.
9) f (x) = 2x
10) f(x) = 4x3
1
Evaluate the function for the given value of x.
18) f (x) = 5x, g(x) = -4x2 - 7, (g - f )(x) = ?
Graph the function by applying an appropriate
reflection.
11) f(x) = -
x
Find f(-x) and determine whether f is odd, even, or
neither.
19) f (x) = -5x5 + 4x3
Graph the equation by plotting points.
12) p(x) = (-x)3
Use interval notation to write the intervals over
which f is (a) increasing, (b) decreasing, and
(c) constant.
20)
Use the graph of y = f (x) below to graph y = f (-x)
13)
Graph the function.
-x - 3 for x -3
21) s(x) =
x + 3 for x > -3
Write an equation of the line satisfying the given
conditions. Write the answer in standard form
with no fractional coefficients.
14) Passes through (1, -5) and is
perpendicular to the line defined by -3x
+ 4y = 6
Find the indicated function and write its domain
in interval notation.
22) n(x) = x - 2, p(x) = x2 - 9x, (p n)(x) =
?
Evaluate the function for the given value of x.
15) f (x) = x2 + 2x, g(x) = 5x - 1, (g f )(2)
=?
Determine whether the graph of the parabola
opens upward or downward and determine the
range.
23) f (x) = -2(x + 1)2 + 4
16) f (x) = -2x, g(x) = |x + 1|, (f g)(-4) = ?
Find the indicated function and write its domain
in interval notation.
17) m(x) = x + 4, n(x) = x - 3, (m n)(x) =
?
Identify the vertex and determine the minimum or
maximum value of the function.
24) f (x) = 2(x + 3)2 - 4
2
Evaluate the function for the indicated value.
32) Evaluate f (-3).
Graph the function and determine the minimum
or maximum value of the function.
25) m(x) = 2(x - 2)2
f (x) =
Sketch the function and determine the axis of
symmetry.
26) f (x) = -(x + 2)2 + 9
10
x+1
-5
x -3
-3 < x 2
x>2
Identify the vertex, axis of symmetry, and
intercepts for the graph of the function.
33) g(x) = x2 - 2x - 8
Determine the x- and y-intercepts for the given
function.
27) f (x) = -2(x + 4)2 + 8
Find the vertex of the parabola by applying the
vertex formula.
1
34) f (x) = x2 + 6x - 1
4
Identify the location and value of any relative
maxima or minima of the function.
28)
Determine the end behavior of the graph of the
function.
35) f (x) = -x2 (7 - x)(3x + 8)4
Find the zeros of the function and state the
multiplicities.
36) f (x) = -2x4 - 17x3 - 36x2
37) f (x) = -5x(4x - 5)(5x - 6)(x + 5)(x - 5)
Determine whether the intermediate value
theorem guarantees that the function has a zero on
the given interval.
38) f (x) = x3 - 2x2 + 16x + 28; [4, 5]
List the possible rational zeros.
29) f (x) = -49x4 + 5x3 + 7x + 14
Use the remainder theorem to determine if the
given number c is a zero of the polynomial.
30) x4 + 9x3 + 15x2 - 15x + 20; c = 5
Sketch the function.
39) f (x) = x3 + 2x2
Determine the number of possible positive and
negative real zeros for the given function.
31) f (x) = -8x7 - 2x4 + 4x3 + 5x2 + 7x + 5
Use synthetic division to divide the polynomials.
2x5 - 6x4 - 15x3 + 67x2 - 71x + 26
40)
x-2
3
A polynomial f (x) and one of its zeros are given.
Factor f (x) as a product of linear factors.
4 - 4i is
41) f (x) = 5x3 - 41x2 + 168x - 32;
a zero
Use synthetic division to divide the polynomials.
x5 - 243
42)
x-3
4
Answer Key
Testname: REVIEW TEST 2- SUMMER 2016
1) 2x + 7y = 13
5
1
2) y = x 6
2
3) x = -6
4) y = 11
5) f(x), I; g(x), III; h(x), II
6)
7) 3x - 5y = -10
8)
5
Answer Key
Testname: REVIEW TEST 2- SUMMER 2016
9)
10)
11)
6
Answer Key
Testname: REVIEW TEST 2- SUMMER 2016
12)
13)
14) 4x + 3y = -11
15) (g f )(2) = 39
16) (f g)(-4) = 24
17) (m n)(x) = x + 1; domain: [-1, )
18) (g - f )(x) = -4x2 - 5x - 7
19) f (-x) = 5x5 - 4x3 ; f is odd.
20) a. (- , -3) (1, )
b. never decreasing
c. (-3, 1)
7
Answer Key
Testname: REVIEW TEST 2- SUMMER 2016
21)
22) (p n)(x) = x2 - 13x + 22; domain (- , )
23) Downward
Range: (- , 4]
24) Vertex: (-3, -4)
Minimum: -4
25) minimum value = 0
8
Answer Key
Testname: REVIEW TEST 2- SUMMER 2016
26) Axis of symmetry: x = -2
27) x-intercepts: (-6, 0) and (-2, 0)
y-intercept: (0, -24)
28) At x = -4, the function has a relative minimum of -5.
At x = 0, the function has a relative maximum of 0.
At x = 4, the function has a relative minimum of -5.
2
2
1
1
29) ±1, ± , ± , ±7, ±2, ±14, ± , ±
7 49
7 49
30) No
31) Positive: 1; Negative: 4 or 2
32) 10
33) Vertex at (1, -9); axis: x = 1; x-intercepts: (-2, 0) and (4, 0); y-intercept: (0, -8)
34) (-12, -37)
35) Down left and up right
9
36) 0 (multiplicity 2), -4 (multiplicity 1), - (multiplicity 1)
2
37) 0,
5 6
, , ± 5 ; each of multiplicity 1
4 5
38) No
9
Answer Key
Testname: REVIEW TEST 2- SUMMER 2016
39)
40) 2x4 - 2x3 - 19x2 + 29x - 13
41) (5x - 1)(x - (4 - 4i))(x - (4 + 4i))
42) x4 + 3x3 + 9x2 + 27x + 81
10