Functions
What degree is a quadratic function?
Degree 2
What transformation has been applied?
y=x^2->y=(x-1)^2
A horizontal translation 1 unit right
Is the following sequence arithmetic, geometric, or neither?
3, 5, 7, 9
What are the non-permissible values for the function:
(1-x^2)/(1+x^2)
None! It is defined everywhere.
What is the general solution to
sinx=1/2
x=pi/2+2pin, 5pi/6+2pin, n in I
Find (g/f)(x)
f(x)=x+2
g(x)=x^2+5x+6
The answer is
(g/f)(x)=x+3
How has the function been transformed?
y=sinx -> y=sin2x
A horizontal stretch by a factor of 1/2
What is the common ratio of the following geometric sequence?
8/9, -2/3, 1/2
r=-3/4
A polynomial has x-intercepts 1 and -4, and a y-intercept of 8. Write its equation in the form:
y=ax^2+bx+c
y=-2x^2-6x+8
Prove the identity:
sinx+cotxcosx=cscx
Answers will vary!
What are the domain and range of:
f(x)=-|x+3|-4
Domain:
(-infty, infty)
Range:
[-infty, -4]
True or false: a vertical stretch can change the x-intercepts of a function.
FALSE!
Determine the 15th term (to 2 decimal places) of the geometric sequence:
15, 12, 9.6,...
t_15=0.66
Is (x+1) a factor of:
P(x)=-7x^4-7x^3-13x^2-8x+5
YES!
P(-1)=0
What are the non-permissible values of:
y=(sinx-1)/(cosx-1)
xne2pin, ninI
Write an equation, in the form y=, for the relation which is the inverse of y=(x+3)^2+1
y=-3+-sqrt(x-1)
The graph of a relation and its inverse are reflections about which line?
The line y=x
Calculate the sum
2/3+2/15+2/75+...
S_infty=5/6
Write in fully factored form:
P(x)=x^3+2x^2-5x-6
P(x)=(x+1)(x-2)(x+3)
Give an exact value for cosine of 105 degrees.
(sqrt2-sqrt6)/4
What is the inverse of y=e^(2x)+1
y=1/2(ln(x-1))
Describe how a function is transformed if the following replacement is made in its equation:
y -> y+3
A vertical translation 3 units DOWN
How many terms are in the series:
sum_(k=3)^87 5(3/4)^(k)
85
Write the equations of all asymptotes of the function:
y=(5x^2)/(x^2+5x+6)
x=-2, x=-3, y=5
What is the sum of the interior angles of a triangle?
180 degrees!