Arithmetic Operations and Functions
Suppose f(x)=5x^2 and g(x)=3x^3. Find f/g
f/g= 5/3x
Is -6 a factor of 720?
Yes
tan(π/3)
√3
Show that 0.2777777 is rational
x=5/18
Without a calculator, find log381
log381= 4
Suppose f(x)=3x-2 and g(x)=(x+2)/(3)
Find f°g
f°g= x
Give the degree of (x6-7x2+8x)(3x4+5x2-8)
Degree is 10
Convert 150° to exact radians
5π/6
True or False?
When dividing two irrational numbers, the answer is irrational.
False
Solve 5x=1013
4.3
Suppose f(x)=3x-2 and g(x)=x3+1
Find g°f(x)
g°f(x)= 27x3-54x2+36x-7
Divide 3087 by 50 using long division
61 R37
Find all solutions to cosx=(-1/2) in the domain 0≤x≤2π
(2π/3) and (4π/3)
Rewrite the equation in lowest terms and give any restrictions:
(6x2+17x+10)/(12x2+16x+5)
(x+2)/(2x+1)
Restrictions: x≠(-5/6) and (-1/2)
Describe the graph without using a calculator:
y=(-1/6)x4
Parabola opening down
Find all solutions to
4-x=√(x-2)
x=3
Find the prime factorization of 680
17*5*23
Find the peak value, frequency, and period of the sine wave I=2.5sin(21600°t), where t is in seconds.
Peak Value= 2.5
Frequency= 60
Period= 1/60
Write the complex fraction as a simple fraction:
((1/x)+(3/x2))/((9/x2)-1)
(1/(3-x))
Simplify:
(48a2b-6c3)/((2ab-2)4c-2)
(3b2c5)/(a2)
Find all solutions to the inequality
cosx<1/2 on the interval 0≤x≤2π
(π/3)<x<(5π/3)
Find the check digit at the end of the given ISBN-10 number:
0-312-08082-XC
4
Give an equation for y=cosx with the following changes:
Phase shift of -π/4, Vertical shift of -6, Amplitude of 2, Period of 3π/2
y=2cos(4/3)(x+(π/4))-6
Solve (8/(x+3))+(x/(x-3))=(-2/(x2-9))
1.728 and -12.728
Restrictions: +/-3
Using the sequence dn=(-8/2) for n=1,2,3,4,5,6
a)Find the first 6 terms
b)Is d increasing, decreasing, or neither?
a) -4,-2,1,-1/2,-1/4,-1/8
b) increasing toward zero