Function ops
g(x) = x - 1 , f(x) = x2 - 4
Find g(-1) + f(-1)
-5
3e-x-8 - 9 = -3
-ln 2 - 8
A stock’s price is rising at the rate of 7% per year, and that it continues to increase at this rate. If the value of one share of this stock is $43 now, find the value of one share of this stock three years from now.?
$52.68
Find the domain, range, x and y intercepts, vertical and horizontal asymptotes
f(x)2/(x-1) + 3
Va: 1 Ha -2
xint: 4 yint: -4
D: (- infinity, 1)U(1, infinity)
R: (- infinity, -2)U(-2, infinity)
1-2tan2 (theta) = -tan2 (theta)
pi/4 (3pi)/4 (5pi)/4 (7pi)/4
g(x) = 2x − 5 h(x) = 4x + 5
Find g(3) − h(3)
-16
-5e-2n-7-10 = 88
ln (78/5+7)/2
A national park has a population of 5000 deer in the year 2016. The deer population is decreasing at the rate of 7% per year. If the population continues to decrease at this rate, how long will it take until the population is only 3000 deer?
7 or 7.039 years
Find the domain, range, x and y intercepts, vertical and horizontal asymptotes
(x - 1)/(-2x2 +6x)
Va: (3,0) Ha: y=0
xint: 0 yint: 0
Domain:( - Infinity, 0)U(0,3)U(3, infinity)
Range:( - infinity, 0)U(0, infinity)
3sin (theta) = sin (theta) + 1 - sin2 (theta)
pi/2 (7pi)/6 (11pi)/6
f (x) = 2x3 − 5x2 g(x) = 2x − 1
Find ( f ⋅ g)(x)
4x4 − 12x3 + 5x2
log5 6 + log5 2x2 = log5 45
{2 , -2}
A video posted on YouTube initially had 80 views as soon as it was posted. The total number of views to date has been increasing exponentially according to the exponential growth function y = 80e^0.12t , where represents time measured in days since the video was posted. How many days does it take until 2500 people have viewed this video?
28.7 days
Find the domain, range, x and y intercepts, vertical and horizontal asymptotes.
f(x) = (x2 + x - 12)/(4x - 16)
Ha: none Va: x = 4, -3
Domain: ( - infinity, -3)U(-3, 4)U(4, - Infinity)
Range: ( - infinity, 0)U( 0, infinity)
xint: -3, yint: 3/4
holes: 4, 7/4
3sin (theta) + 2sin2 (theta) = -1
(7pi)/6 (3pi)/2 (11pi)/6
h(a) = 3a g(a) = −a3 − 3
Find ( h/g) (a)
(3a)/(-a^3-3)
ln (-5x - 2) - ln 8 = 3
(-8e^3-2)/5
A statistician creates a website to analyze sports statistics. His business plan states that his goal is to accumulate 50,000 followers by the end of 2 years (24 months from now). He hopes that if he achieves this goal his site will be purchased by a sports news outlet. The initial user base of people signed up as a result of pre-launch advertising is 400 people. Find the monthly growth rate needed if the user base is to accumulate to 50,000 users at the end of 24 months.
The website’s user base needs to increase at the rate of 22.28% per month in order to accumulate 50,000 users by the end of 24 months.
Find the domain, range, x and y intercepts, vertical and horizontal asymptotes.
F(x) = (x2 + 3x)/(x2 + 2x - 3)
Ha: y=1 Va: x = 1
Hole: (-3, 3/4)
D: ( - infinity, -3)U(-3,1)U(1, infinity)
R: ( - infinity, 3/4)U(3/4, 1)U(1, infinity)
xint: 0, 0 yint: 0, 0
sin^2 (theta) + 2 - cos^2 (theta) = 3sin (theta)
pi/6 pi/2 (5pi)/6
g(t) = 2t + 5 f (t) = −t2 + 5
Find (g + f )(t)
−t2 + 2t + 10
ln 2 - ln (4x + 7) = 4
(2-7e^4)/(4e^4)
A fact sheet on caffeine dependence from Johns Hopkins Medical Center states that the half life of caffeine in the body is between 4 and 6 hours. Assuming that the typical half life of caffeine in the body is 5 hours for the average person and that a typical cup of coffee has 120 mg of caffeine.
After 12.9 hours, 20 mg of caffeine remains in the body.
Find the domain, range, x and y intercepts, vertical and horizontal asymptotes.
f(x) = (x2 + x2)/(-3x2 + 3x)
Ha: 1/3 Va: 1
D: (- infinity, 1)U(1, infinity)
R: (- infinity, - 1/3)U(-1/3, infinity)
yint: 0 xint: 0
3sin (theta) sqrt3sin (Theta) + 3cos (theta) + 3sin (theta)
(2pi)/3 (5pi)/3