Talk the Talk
Piece It Together
Combos
Function Inception
Push It to
the Limit
the Limit
100
In this type of function the OUTPUT of the inner function becomes the INPUT of the outer function.
Composite (Composition)
f(g(x))
100
f(4)=9
100
Find (g-f)(4)=
(g-f)(4)=-4
100
Evaluate f(g(4))=
g(f(-4))=6
100
Find the LIMIT
lim_(x->-8)f(x)=
lim_(x->-8)f(x)=-6
200
Piecewise functions have two or more of these...each with their own specific interval.
Sub-functions
200
Find
f'(17)=
f'(17)=-1/2
This is the DERIVATIVE or SLOPE at the point t=17.
This means the acceleration at 17 seconds is decreasing at a rate of 0.5 m/s2 (object is slowing down).
200
Find f(x)*g(x) in STANDARD form.
f(x)=3x-4 and g(x)=-x+5
(f*g)(x)=-3x^2+19x-20
200
Find (gof)(x) in STANDARD form.
f(x)=sqrt(x+10) and g(x)=3x^2-10
g(f(x))=3x+20
200
The limit does not exist (DNE).
300
What is this LIMIT statement used to find?
Derivative
f'(x)
(the SLOPE of a line TANGENT to a point)
300
Write the equation of the PIECEWISE function.
c(g)={(25;( 0<=g<=2)),(10g+5;(g>=2)):}
300
Find the DOMAIN of the function f(x)/g(x) if
f(x)=3x-2 and g(x)=sqrt(x+2)
x> -2
300
Find (fog)(x) in STANDARD form.
f(x)=x^2-x+4 and g(x)=2x+5
f(g(x))=4x^2+18x+24
300
lim_(x->-1)(f(x)-h(x))=1
400
Mathematical term for the AREA between the graph of a function and the X-AXIS over a specific interval. It's symbol is
int_a^b
Integral
400
Find
int_0^25 V(t) dt
int_0^25V(t)dt=200
This is the INTEGRAL or area between the graph and the x-axis.
This means the displacement after 25 seconds was 200 meters.
400
DAILY DOUBLE!! This question is worth 800!!
If f(x)=2x-2 and g(x)=x2 evaluate the expression:
(f(5)/(f(3)g(3)-g(-2)))^f(1/2)
(f(5)/(f(3)g(3)-g(-2)))^f(1/2)=4
Order of Operations...thanks PEMDAS!
400
DECOMPOSE the function h(x) into
two distinct functions f(x) and g(x).
h(x)=1/(3x-5)
Multiple answers.
400
DAILY DOUBLE!!! This question is worth 800!!
A secant line intersects f(x) at two points, x=3 and x=t, where t cannot equal 3. Find the SLOPE of the SECANT line in terms of t. Your answer should be simplified.
f(x)=x^2+5x
m=(triangley)/(trianglex)
m=(f(t)-f(3))/(t-3)
m=(t^2+5t-(3^2+5(3)))/(t-3)
m=(t^2+5t-24)/(t-3)
m=((t-3)(t+8))/(t-3)
m=t+8
500
If the LIMIT for a function does not exist, the function is said to be...
Discontinuous (at that point)
500
Find the INPUT(s) that would create g(x)=1
g(-2)=1 and g(2)=1
500
If it costs a computer company a fixed cost of $60,000 and $45 per computer for manufacturing, what formula represents the profit the company is making if the revenue is $65 per computer?
Profit = Revenue - Cost
P(x) = R(x) - C(x)
P(x) = 65x - (45x + 60,000)
P(x) = 20x - 60,000
500
Find (fog)(x) and simplify.
State any restrictions on the DOMAIN.
f(x)=1/(x+2) and g(x)=4/x
(fog)(x)=x/(2x+4)
x cannot equal 0 or -2
500
Find f prime of x...show all algebraic steps.
f(x)=-x^2
Instructor (Jeopardy host) looks at process.
(-(x+trianglex)^2-(-x^2))/(trianglex)
(-(x+trianglex)(x+trianglex0)+x^2)/(trianglex)
(-x^2-2xtrianglex-trianglex^2+x^2)/(trianglex)
(triangle x(-2x-trianglex))/(triangle x)
-2x-triangle x
-2x