Test 1 Content
Solve the equation x2 +5x -6=0
What are x=2, x=3
if F(x)= 3x-5, find F(4)
what is 7?
Determine the end behavior of f(x)=-3x5 +2x3 -x +7
what is f(x)--> -inf as x-->+inf and f(x)-->inf+ as x--> -inf
solve: 2x=16
what is x=4
explain how the following graphs shift; draw it out on board
a- y=√(x+2) -5
b- y=(x-3)3
a- shift left two, down 5
b- shift right 3
Solve the equation √(x+3)=5
what is x=22
The graph of y=x2-4x +3 intersects the x-axis at what points? what is the y-intercept
what are x=1,3? what is (0,3)?
What is the vertex form and how do you find it
f(x)=a(x-h)2 + k, where (h,k) is the vertex
find it by (-b/2a, f(-b/2a))
solve
5e2x=20
what is ln(4)/2
or 0.693
what is the quadratic equation
[-b+/-√(b2-4ac)]/2a
Simplify and write in standard form: (3 +2i) + (5-4i)
what is 8-2i
What are the domain and range of this graph?
What is d=[-3,-1)U[0,3) and r=[-2, inf+)
divide x3-4x2+x+6 by x-2 using synthetic division. what is the quotient and remainder?
what is x2-2x-3, R=0
evaluate log381=x
what is x=4
what are the two interest formulas we use? what are the variables and when do we use one vs other
Continuous: A= Pert
a= final amount, p=principal amt, e is on calc (2.718...), r= rate as decimal, t=time in years
A=P(1 + r/n)nt
every variable the same; n=number of times compounded
Use 1st if problem says compounded continuously, use 2nd if it gives you a number of times the amt is compounded
Solve the inequality 2x-7≤5
what is x≤6
Find the average rate of change of f(x)=x2+2x from x=1 to x=4
What is 7
f(x)=(x2-9)/(x2-x-6)
What are the holes, vertical and horizontal asymptotes (if any of these) of this graph?
simplified: f(x)=(x+3)/(x+2)
hole at (3,6/5)
vertical asymptote x=-2
horizontal asymptote y=1
condense
logx+2logy− 1/2logz
what is log[(xy2)/√z)]
explain the two "problems" a function can have that prevents the domain from being (-inf, inf+).
What are they, and how do we find the domain?
two problems are square roots and fractions
if square root, set expression under the root greater than or equal to zero. this tells you what the domain CAN be
if fraction, set DENOM expression to "can't equal 0." this tells you what the domain CAN'T be.
if a square root in denominator: set expression under root to greater than zero. This tells you what the domain can be
Find the center of a circle given by (x-3)2 +(y+4)2+4=0
What is center = (3,-4), and radius=2
Let f(x)=2x+3 and g(x)=x-1
a)find (f+g)(x)
b) find the inverse of f(x)
what is
a)3x+2
b) (x-3)/2
divide the function f(x)=2x3+5x2-4x-3 by x+3 using long division
is this a slant asymptote of f(x)? why
what is 2x2-x-1, R=0
yes because the remainder of the function divided by the quotient is zero
solve
{x2+y2=25
{y=x+1
what are (x,)= (-4,-3) and (3,4)
solve
x4-5x2+4=0
what information do we get from this if it were a graph?
u sub:
x=-2,-1,1,2
x intercepts