Domain & Range
f(x)=sqrt(x)+4
Domain: [0, +infinity)
Range: [4, +infinity)
f(x)=sqrt(x)+4
x-intercept: NONE
y-intercept: (0,4)
sqrt(x-4)=5
x=29
The equation represents the time (seconds) and height (feet) it takes to drop an object on earth. A rescue package drops from a height of 600 feet. How many seconds does it take for the package to reach the ground? Round two decimal places.
t=sqrt(h)/4
t=6.12 seconds
What are the two types of radicals we have focused on for this unit?
Square roots and Cube roots
g(x)=root3(x-8)+3
Domain: All real numbers
Range: All real numbers
q(x)=10-5sqrt(x)
x-intercept: (4,0)
y-intercept: (0,10)
-8+sqrt(5w-5)=-3
w=6
The equation represents the time (seconds) and height (feet) it takes to drop an object on earth. If it takes 25.32 seconds for the package to hit the ground, determine the height it was dropped? Round two decimal places.
t=sqrt(h)/4
It was dropped from 10,257.64 feet
What is the first step you need to do in order to solve for an equation with a radical?
Isolate the radical!
m(x)=3sqrt(x+2)-5
Domain:[-3, +infinity)
Range: [-5, +infinity)
w(x)=sqrt(x+4)+5
x-intercept: NONE
y-intercept: (0,7)
root3(x+6)=root3((x^2)+8x+16)
x=-5 & x=-2
A right triangle has a hypotenuse of 11 and its base is 5. What is the area of the triangle? Round your answer to two decimal places.
Area: 24.94
Explain how you would find the domain and range of t(x)?
t(x)=10+3sqrt(25x)
1. Put in the correct form & simplify the square root of 25
2. Identify a, h, and k
3. Domain uses h-value [0, inf.)
4. Range uses k-value [10, inf.),
It goes to positive infinity because the a-value is positive
p(x)=-4sqrt(x-3)+7
Domain: [3, +infinity)
Range: (-infinity, 7]
r(x)=4+2root3(x-1)
x-intercept: (-7,0)
y-intercept: (0,2)
2+sqrt(x+10)=x
x= 6
x=-1 (extraneous)
The approximate antler length L (in inches) of a deer can be modeled by the equation below where t is the age in years of the deer. If Debby the deer has an antler length of 36 inches, what is her age? Round to the nearest year.
l=9root3(t)+15
Debby the deer would be 13 years old
How do you set up your equation to solve for x-intercepts and y-intercepts?
x-intercepts: Set the y variable equal to zero
y-intercepts: Set the x variable(s) equal to zero
t(x)=10-5sqrt(x)
Domain: [0, +infinity)
Range: (-infinity, 10]
g(x)=root3(x-8)+3
x-intercept: (-19,0)
y-intercept: (0,1)
root3(-3(x^2)+2)=-1
x=1 & x=-1
In Six Flags, the Batman ride can model the velocity v in m/s, r as the radius in meters around each curve, and a is the acceleration in m/s2. If the ride has a maximum acceleration of 30m/s2 and the cars on the ride have a maximum velocity of 12m/s, what is the smallest radius that any curve on the ride may have?
v=sqrt(ar)
The smallest radius that any curve on the ride may have is about 4.8 meters
What is an extraneous solution and how do you check for them?
An extraneous solution is a solution that does not satisfy the original equation. You can check for an extraneous solution by plugging in the value back into the original equation and figuring out if it makes a balanced/true equation.