Functions
Given f(x)=3x2+4x-6, determine f(5)
89
State the restrictions of the following rational expression: 3x2/x2(3x-4)
x =/= 0, 4/3
Determine the roots of:
f(x)=3x2-16x+21
x = 3, 7/3
Determine the transformations applied to the following:
f(x)=2×3(x−1)
The function is vertically stretched by a factor of 2.
The function is shifted 1 unit to the right.
sin2(x)+cos2(x)=1 is known as what?
The Pythagorean Identity
Determine the domain and range for the following function: f(x) = 3root(x+2)
domain: {x all real numbers | greater than or equal to -2),
range {f(x) all real numbers, greater than or equal to 0}
State the Lowest Common Denominator:
2n/(n-4)+3(3n-2)
What is: (n-4)(3n-2)
Without Evaluating, how many roots does the following equation have?
f(x)=2x2+4x+5
0, or undefined.
Find the value x such that the following is true:
5(x+9)=25(2x)
x=3
What is the amplitude and period of the following function:
f(x)=-5sin(3x)
amplitude: 5
period: 120*
For the following function, f(X)=4root(x+4)+12, determine f(-2/3), give an exact value.
((4root30)/3)+12
Simplify: (6x2-19x+3) / (4x2-36)
6x-1/4(x+3)
Determine the min or max coordinates of the following quadratic: f(x)=x2-6x+8
coordinates: (x,y)=(3,-1)
An E. coli colony triples its population every day for 7 days. There are currently 40 bacteria in the sample. Determine the model for this growth, and determine the number of bacteria after 7 days.
g(t)=40(3)t
g(7)= 87480
provide all the solutions for x such that cos= 1/2
(0*<x<360*)
x=60, 300 degrees.
Given the function f(x)= root(3x+5) state the inverse.
f-1(x)= (x2-5)/3
Simplify: (2x2+5x+2/4x2-1) X (2x2+x-1/x2+x-2)
(x+1)/(x-1)
Determine the vertex form of the following quadratic:
f(x)=3x2-12x+13
f(x)=3(x−2)2+1
The initial tire pressure is 85 PSI (pounds per square inch). When the nail punctures the tire, it causes a slow air leak. The pressure of the tire decreases by rate of 3.5% per hour. Write an equation to model the tire pressure.
P(t)=85(0.965)t
The sine function reflects about the x axis, VC by a factor of 2, HS by a factor of 3, and shifts 60* right, and shifts up 3 units. Determine the function.
f(x)=-2sin(3(x-60*))+3
Given the functions f(x)=2x+3and g(x)=x2−1, find the composite function (f∘g)(x) and determine its value at x=2.
(f∘g)(x)=2x2+1
(f∘g)(2)=9
Simplify: (x2+3x-4/x2+2x-35) ÷ (x2+2x-48/x2+3x-18)
=(x+6)(x-3)/(x+7)(x-6)
Determine the value of k such that the quadratic has one real root:
f(x)= 2x2+kx+3
k= (+/-) 2root6
In 1955, there were 550 subscribers to the OurNews paper. Every year, the subscriber count increased by 11%. Provide an equation for this model, and determine the number of subscribers by the year 2002 (round to the nearest person).
S(t)=550(1.11)t
S(47)=12439
A Ferris wheel has a diameter of 17m. You board the bottom of the ferris wheel from a platform 2m off the ground. If it takes 25 seconds to reach the top, determine the equation for the height of the rider with respect to time.