Math1314-TestReview2-Spring2016 Name__________________________________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
1) Is the point (-5, -3) on the circle defined by (x + 2)2 + (y - 1)2 = 25
A) Yes
1)
B) No
Determine the center and radius of the circle.
2) (x - 2)2 + (y - 5)2 = 75
2)
A)
Center: (2, 5); Radius: 5 3
B) Center: (-2, -5); Radius: 75
C)
Center: (-2, -5); Radius: 5 3
D) Center: (2, 5); Radius: 75
Use the given information about a circle to find its equation.
3) center (-7, -9) and diameter 10
A) (x +
7)2
+ (y +
9)2
B) (x +
= 100
C) (x - 7)2 + (y - 9)2 = 25
3)
7)2
+ (y +
9)2
= 25
D) (x - 7)2 + (y - 9)2 = 100
1
Write the equation in standard form to find the center and radius of the circle. Then sketch the graph.
4) x2
+ y2 + 4x - 21 = 0
A) (x +
2)2
+
y2
4)
B) (x +
= 25
C) (x + 2)2 + y2 = 16
2)2
+
y2
= 25
D) (x + 2)2 + y2 = 16
2
For the given relation, write the domain, write the range, and determine if the relation defines y as a
function of x.
5)
5)
A) Domain: {-4, 1, 4}; Range: {-3, -1, 4}; not a function
B) Domain: {-3, -1, 4}; Range: {-4, 1, 4}; not a function
C) Domain: {-4, 1, 4}; Range: {-3, -1, 4}; function
D) Domain: {-3, -1, 4}; Range: {-4, 1, 4}; function
Determine whether the relation defines y as a function of x.
6)
6)
A) Not a function
B) Function
Evaluate the function for the indicated value, then simplify.
7) f (x) = -5x - 5; find f (a - 3), then simplify as much as possible.
A) a + 10
B) -5a - 8
C) -5a + 10
7)
D) a - 13
8) f (x) = -4x2 - 2x; find f (-4)
A) -66
8)
B) 264
C) 24
3
D) -56
Determine the x- and y-intercepts for the given function.
x-8
9) f (x) =
A) x-intercept: (64, 0); y-intercept: (0, -8)
B) x-intercept: (-8, 0); y-intercept: (0, 64)
C) x-intercept: (-8, 0); y-intercepts: (0, -64) and (0, 64)
D) x-intercepts: (-64, 0) and (64, 0); y-intercept: (0, -8)
9)
Determine the domain and range of the function.
10)
10)
A) Domain: (- , -1]; Range: [-4,
B) Domain: (-4,
C) Domain: [-4,
D) Domain: [-4,
)
]); Range [-3, - )
); Range: (- , -1)
); Range: (- , -1]
Write the domain in interval notation.
x-1
11) f(x) =
x-8
A) (- , -8)
C) (- , 1)
12) f(x) =
11)
B) (- , -1)
(-8, )
(1, )
D) (- , 8)
(-1, )
(8, )
8
12)
6-x
A) [6,
)
B) (- , 6]
C) (- , 6)
D) (6,
)
Find the slope of the ramp pictured below.
13)
13)
A) -88
B)
25
3
C) 88
4
D)
3
25
Determine the slope of the line passing through the given points.
1 3
3 3
,
and - ,
14)
2 2
2 5
A) m = -
9
10
B) m =
20
9
C) m =
9
20
14)
D) m =
Write the equation in slope-intercept form and determine the slope and y-intercept.
15) -4x = -3y - 12
4
4
A) y = - x + 12; slope: - ; y-intercept: (0, 12)
3
3
B) y = -
9
10
15)
4
4
x - 4; slope: - ; y-intercept: (0, -4)
3
3
C) y =
4
4
x - 4; slope: ; y-intercept: (0, -4)
3
3
D) y =
4
4
x + 12; slope: ; y-intercept: (0, 12)
3
3
Use the slope-intercept form to write an equation of the line that passes through the given points. Use
function notation where y = f(x).
16) (4, 5) and (2, 13)
16)
A) f(x) = -4x + 11
B) f(x) = -4x - 21
C) f(x) = 4x + 11
D) f(x) = -4x + 21
5
Find the slope of the secant line indicated with a dashed line.
17)
17)
A) m =
4
7
B) m =
7
4
C) m = -
7
4
D) m = -
Determine the average rate of change of the function on the given interval.
18) f(x) = 2x2 + 1 on [1, 3]
1
3
A)
B) 8
C)
D) -8
2
2
4
7
18)
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).
19) Passes through (-5, 2) and the slope is undefined.
19)
A) y = 2
B) y = x - 5
C) y = x + 2
D) x = -5
Write an equation of the line satisfying the given conditions. Write the answer in slope-intercept form.
20) The line passes through the point (6, -14) and has a slope of -3.
20)
A) y = 3x - 14
B) y = -3x - 14
C) y = -3x + 4
D) y = -3x + 6
Write an equation of the line satisfying the given conditions. Write the answer in standard form with no
fractional coefficients.
21) Passes through (-5, -1) and is parallel to the line defined by 3x - 5y = 9
21)
A) 3x - 5y = -6
B) 3x - 5y = -1
C) 3x - 5y = -5
D) 3x - 5y = -10
6
Use translations to graph the given function.
22) f (x) = |x| - 2
22)
A)
B)
C)
D)
7
Sketch the graph using transformations of a parent function (without a table of values).
23) r(x) =
23)
x+4
A)
B)
C)
D)
8
24) a(x) = (x - 1)2
24)
A)
B)
C)
D)
9
Use translations to graph the given function.
25) a(x) = x + 3 - 2
25)
A)
B)
C)
D)
10
Solve the problem.
26) Use the graph of y = f (x) below to graph y = 2f (x)
A)
B)
C)
D)
11
26)
Graph the function by applying an appropriate reflection.
27) f(x) = -
27)
x
A)
B)
C)
D)
12
Use transformations to graph the given function.
28) f(x) = -(x + 1)2 + 3
28)
A)
B)
C)
D)
Determine whether the graph of the equation is symmetric with respect to the x-axis, y-axis, origin, or
none of these.
29) y = -x4 - x2
29)
A) origin
B) x-axis
C) y-axis
Find f(-x) and determine whether f is odd, even, or neither.
30) f (x) = -5x5 + 4x3
-5x5
4x3 ; f
A)
f (-x) =
B)
f (-x) = 5x5 - 4x3 ; f is odd.
C)
f (-x) = 5x5 - 4x3 ; f is even.
D)
f (-x) = 5x5 - 4x3 ; f is neither odd nor even.
-
is odd.
13
D) none of these
30)
Use interval notation to write the intervals over which f is (a) increasing, (b) decreasing, and (c) constant.
31)
31)
A) a. (- , 2)
B) a. never increasing
(2, )
b. never decreasing
c. (-3, 1)
C) a. (-5, )
b. (- , -5)
c. never constant
b. (- , -3) (1, )
c. (-3, 1)
D) a. (- , -3) (1, )
b. never decreasing
c. (-3, 1)
14
Identify the location and value of any relative maxima or minima of the function.
32)
32)
A) At x = -5.7, the function has a relative minimum of 0.
At x = 0, the function has a relative maximum of 0.
At x = 5.7, the function has a relative minimum of 0.
B) At x = -4, the function has a relative minimum of 0.
At x = 0, the function has a relative maximum of 0.
At x = 4, the function has a relative minimum of 0.
C) 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.
D) At x = -4, the function has a relative minimum of -5.
At x = 4, the function has a relative minimum of -5.
Evaluate the function for the given value of x.
f
(2) = ?
33) f (x) = 4x, g(x) = |x - 6|,
g
A)
34)
Find
f
1
(2) =
g
2
B)
33)
f
1
(2) = g
2
C)
f
(2) = - 2
g
D)
f
(2) = 2
g
f (x) = 5x, g(x) = -4x2 - 7, (g - f )(x) = ?
34)
A)
(g - f )(x) = -4x2 - 5x + 7
B)
(g - f )(x) = -4x2 + 5x + 7
C)
(g - f )(x) = -4x2 - 5x - 7
D)
(g - f )(x) = -4x2 + 5x - 7
f(x + h) - f(x)
for the given function.
h
35)
f (x) = x2 + 2x.
A) 2x + 2
35)
B)
2xh + h2 + 2
C) 2x + h + 2
15
D) 1
Evaluate the function for the given value of x.
36) f (x) = x2 + 2x, g(x) = 5x - 1, (g f )(2) = ?
A) (g f )(2) = 39
C) (g f )(2) = 32
36)
B) (g
f )(2) = 72
D) (g f )(2) = 99
Refer to the values of k(x) and p(x) in the table, and evaluate the function for the given value of x.
37)
37)
x
-4
-1
3
4
k(x)
-5
4
-2
-1
p(x)
-4
3
-5
1
(p k)(-1)
A) -5
B) -2
C) -4
D) 1
Use the definition of a one-to-one function to determine if the function is one-to-one.
38) f (x) = |x + 1|
A) Yes
B) No
A one-to-one function is given. Write an expression for the inverse function.
39) f (x) = 5x3 - 7.
x+7
A) f -1(x) =
3
39)
x+7
B) f -1(x) =
5
5
x+7
C) f -1(x) = 3
x-7
D) f -1(x) =
5
40) f (x) =
38)
5
x+5
x-1
40)
5 + 1x
A) f -1(x) =
x+1
B) f -1(x) =
5 - 1x
C) f -1(x) =
x-1
D) f -1(x) =
x-5
x-1
x+5
x+1
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Answer Key
Testname: UNTITLED1
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A
A
B
A
A
B
C
D
A
D
D
C
D
C
C
D
B
B
D
C
D
C
D
C
A
A
C
A
C
B
D
C
D
C
C
A
D
B
C
A
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