Functions & Properties
Given: f(x)=4x+2 ; g(x)=x2-1
what is (f+g)(x)?
(f+g)(x)=x2+4x+1
Describe the end behaviors of the graphs:
a) -x2
b) x3
c) -x5
(can use arrows)
a) down, down
b) down, up
c) up, down
Find the degree, leading coefficient, and the leading term of the function:
g(x)=(4x2+x)/(6x)
degree: 1; leading coeff.: 2/3; leading term: 2/3x
What is the domain of f(x)=log(4x-7)?
(7/4, ∞)
If you travel at a constant speed of 2mph for 2 hours, and them 4mph for 3 hours, what foes the piecewise function and/or graph look like?
x=2 for (0, 2), x=4 for (2, 5)
Find the domain in interval notation:
f(x)=(√x)/(x-4)
[0, 4)U(4, ∞)
Graph the inverse of h(x)=(x-1)2
Graph of y=(√x)+1 (sqrt graph up one)
Find all possible rational roots:
t(x)=3x3+2x2-4x+9
+/- 1, 1/3, 3, 9
What is the assumed base for log(x)? What is the assumed base for ln(x)?
log(x): base 10
ln(x): base e
One shipment of strawberries and apples weighs 100lbs total. If apples cost $2/lb and strawberries cost $4.50/lb, and the total cost for the shipment was $400, how many pounds of apples and strawberries were bought?
Apples: 20lbs
Strawberries: 80lbs
Are the following functions?
a) f(x)=(x)/(x2+1)
b) g(x)=+/- (√x-2)
c) h(x)= x3-2x2+1
a) yes; b) no; c) yes
Describe the transformations for:
f(x)=-(x-2)2+4
Reflect across x-axis, right 2, up 4
Find the horizontal and vertical asymptote(s):
f(x)=(x+1)/(x2+4x+3)
horizontal: y=0; vertical: x=-3
log(a3b2/c4)
3log(a)+2log(b)-4log(c)
A ball is thrown from the top of a ledge of height 20ft. The graph of its movement with respect to time is represented by
x(t)=-t2+15t+20
When does the ball hit the ground? (When is x=0?)
(Give exact or approximate answer)
Exact answer: (-15-√305)/(-2)
Approximate: 16.23
Given a(x)=x2+4x b(x)=x+3
Find a(b(x)) or (aob)(x)
a(b(x))=x2+10x+21
Given g(x)=x-7 find the equation for g(x) with a horizontal stretch by 1/2, horizontal shift left 2, vertical shift up 9
g(x)= (1/2x+2)+2
Use synthetic division to determine if 2 is a solution (zero, root, etc.) to the following:
v(x)=x3+x2-2x-4
No, get a remainder of 4
Solve for x:
4(-2x-1)=16
x=-3/2
If you have $2184 in an account at the end of 8 years with a 4% interest rate, how much money did you put into the account initially? Round to the nearest dollar.
Hint: Using SIMPLE interest
A=Pert
Find f-1(x) for f(x)=(x)/(x+1)
f-1(x)=(x)/(1-x)
Sketch the graph for a(x)=x(x+1)2(x-3)
End behavior is positive on both sides, touches at x=-1, crosses at x=0, crosses at x=3.
Use long division to determine the remainder of the following:
(x3+4x2-2x+1)/(x2+x+1)
Remainder= -6x-2
Solve for x:
12=log4(3x+2)+9
x=62/3
Vick puts $1200 into a savings account at a 7% interest rate compounded every 3 months. Later, he checked and saw his account was now at $18000. How long did this take? Round to the nearest year.
Hint: Use COMPOUND interest
A=P(1+r/n)nt
Approximately 39 years