Download Part 2 of the Midterm Review Study Guide, which includes Chapter P

Chapter P Test
Name___________________________________
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Simplify the expression. Assume that the variables in the denominator are nonzero.
x-3 y4 -3
1)
y4x-5 -4
2)
1)
(2x3 )2 z 5
2z7
2)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the center and radius of the circle.
3) (x - 4)2 + (y - 1)2 = 49
A) (4, 1), r = 7
B) (-4, -1), r = 49
C) (1, 4), r = 7
Use interval notation to describe the interval of real numbers.
4) x is greater than or equal to -2 and less than or equal to 2.
A) [-2, 2]
B) [-2, 2)
C) (-2, 2)
D) (-1, -4), r = 49
D) (-2, 2]
Solve the problem.
5) A flare fired from the bottom of a gorge is visible only when the flare is above the rim. If it is fired
with an initial velocity of 160 ft/sec, and the gorge is 384 ft deep, during what interval can the flare
be seen? (h = -16t2 + vot + ho.)
A) 12 < t < 14
B) 4 < t < 6
C) 0 < t < 4
1
D) 8 < t < 10
3)
4)
5)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Write the product in standard form.
6) (7 + 8i)(7 - 5i)
6)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Write the sum or difference in the standard form a + bi.
7) i2 + 5 - 2 + i3
A) 2 + i
B) 6 - i
C) 2 - i
7)
D) 6 + i
Write the expression in standard form.
8+ i
8)
-6 - 2i
A) -
5
1
- i
4
4
B)
8)
1
i
4
C) -
5
4
D) -
5
1
+ i
4
4
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Find the distance between the points.
9) (6, -6) (4, -2)
9)
Find a slope-intercept form equation for the line.
10) Through the points (2, 6) and (-2, 9)
10)
2
Determine the equation of the line described. Put answer in the slope-intercept form, if possible.
11) Through (-8, -5), parallel to 7x + 6y = -32
12) Through (7, -6), perpendicular to -3x - 7y = 21
11)
12)
Use a method of your choice to solve the equation.
13) 4x - 7 = 4
13)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
14)
x-4
=3
x+5
A) x = -
14)
11
2
B) x = -
15
2
C) x =
15) x2 - 1 = x + 8
A) x = 0
C) x = -3.04 or x = 3.04
11
2
D) x = -
19
2
15)
B) x = -3.54 or x = 2.54
D) x = -2.54 or x = 3.54
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Solve the equation.
16) x2 + x + 6 = 0
16)
3
Write the expression in the form bi, where b is a real number.
17) -245
17)
Solve the inequality algebraically. Write the solution in interval notation.
18) 8x + 1 < 11
18)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve the inequality. Use algebra to solve the corresponding equation.
19) x2 - 4x - 5 < 0
A) (- , -1)
B) (-1, 5)
C) (- , -1)
(5, )
19)
D) (5, )
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
20) x2 - 5x
20)
-6
4
Name:_________________________ Chapter 1 Review Packet / Study Guide Find the domain of the given functions and write in interval notation. 1) f(x) = √
2) f(x) = √
√
√
3) f(x) = Use the graphs or equations to find the local maxima and minima, and the intervals which are increasing, decreasing, or constant. 4) 5) 4) ____________________________________ 5)_________________________________________ 6) f(x) = 4
1 8) f(x) = 6
2 7) f(x) = |2x+5|+|2x 7| 14 7)_________________________ 8)_________________________ 6)_________________________ Graph the function and determine where the point of discontinuity is (write as “x =”). If there is a discontinuity, tell whether it is removable or non‐removable. 9) f(x) = 10) f(x) = 11) f(x) = 9)_________________________ 10)_________________________ 11)_________________________ | |
12) f(x) = 13) f(x) = 14) f(x) = 12)_________________________ 13)_________________________ 14)_________________________ Find the asymptote(s) of the given function. Write asymptotes as “x =” or “y =” 16) f(x) = 15) ______________________ 18) ______________________ 15) f(x) = 17) f(x) = 16)____________________ 17)_______________________ 19) f(x) = 20) f(x) = 19)____________________ 20)_______________________ 23) f(x) = 23)_______________________ 18) f(x) = Find the inverse of the following functions. 22) f(x) = √2
21) ______________________ 22)____________________ 21) f(x) = 2
3 3 Find the inverse of the following functions. 24) f(x) = 25) f(x) = 24) ______________________ 25)____________________ 26) f(x) = 26)_______________________ Perform the requested operations given the functions below: a(x) = 7x + 14 b(x) = 4x – 1 c(x) = 3x + 2 d(x) = x‐1 e(x) = 28) g(h(x)) 29) a(h(‐0.5)) 30) e(f(x)) f(x) = g(x) = h(x) = √
27) c(b(x)) Determine if the following functions are even, odd, or neither. 31) f(x) = 6 32) f(x) = 33) f(x) = 33) f(x) = 5x + 17 2 Evaluate the piecewise function, f(x), for the given values of x. 34) f( ‐2) 35) f( 0.5) 37. Graph the piecewise function from #34 to 36, f(x), below: 36) f(6) Evaluate the piecewise function, k(x), for the given values of x. 38) k( ‐2) 39) k( 0.5) 41. Graph the piecewise function for #38 to 40, k(x), below: 40) k(0)