Average Rate of Change
Find the average rate of change of g(x)=3x from x=0 to x=4.
3
Find the difference quotient of f(x)=5x2−6.
10x +5h
If g(x)=2x2, h(x)=3x, find h+g.
2x2+3x
If f(x)=x−5, g(x)=3x2−x, find f⋅g.
(x−5)(3x2−x)=3x3−16x2+5x.
If r(x)=2x+1, s(x)=−2x2−2, find s(r(−3)).
r(−3)=−5
⇒s(r(−3))
=s(−5)
=−2(25)−2
=−52.
Find the average rate of change of g(x)=2x3−2x2−3 from x=1 to x=2.
8
Find the difference quotient of f(x)=−9x+1.
-9
If g(x)=2x2, h(x)=3x, find h⋅g.
(3x)(2x2)=6x3
Find the domain of g/f where f(x)=x−5, g(x)=3x2−x.
all reals x≠5
If f(x)=x+1, g(x)=x2, find f(g(2)).
f(g(2))=f(4)=5.
A rocket’s height is given by: H(0)=0, H(2.3)=60.
Find the average rate of change from 0 to 2.3 seconds.
26.087 m/s
Simplify the difference quotient for f(x)=x2+3x.
2x+h+3
If h(x)=x−8, g(x)=(x+3)(x+4), find h/g.
h/g=x−8/(x+3)(x+4).
A car rental costs S=15.75+0.60M. Insurance costs I=5.70+0.25M. Write C(M), the total cost.
21.45+0.85M.
If f(x)=x+1, g(x)=x2, find g(f(2)).
g(f(2))=g(3)=9.
For f(x)=x2+2x, find the average rate of change from x=−1 to x=3.
4
For f(x)=2x2−4x+1, simplify the difference quotient.
4x+2h-4
For h(x)=x−8, g(x)=(x+3)(x+4), state the values of x that are not in the domain.
Not in domain when denominator =0: x≠−3,−4
Sales tax is T(C)=1.07C. Write (T∘C)(M) and find the cost for M=80.
(T∘C)(M)=1.07(21.45+0.85M)=22.9515+0.9095M.
If f(x)=2x+14, g(x)=x−2, find f∘g(x).
(f∘g)(x)=2(x−2)+14=2x+10.
Which interval shows a greater average rate of change for f(x)=x3: from x=0 to x=2 or from x=2 to x=4?
(0,2)= 4
(2,4)= 28
Greater on (2,4)
If f(x)=x2, use the difference quotient to estimate the slope at x=2.
2x+h
slope= 4
If h(x)=3x2−5, g(x)=−6x+2, simplify h/g and give its domain.
3x2−5/-6x+2 with domain x=1/3
Suppose P(x)=2x+1, Q(x)=x2−4. Write P(Q(x))+Q(P(x)).
P(Q(x))=2(x2−4)+1=2x2−7
Q(P(x))=(2x+1)2−4=4x2+4x−3Q(P(x))=(2x+1)2−4=4x2+4x−3
Sum: 6x2+4x−106x2+4x−10.
If g(x)=x−4/x+3, h(x)=4x−7, find the domain of g∘h(x).
(g∘h)(x)=(4x−7)−4/(4x−7)+3
=4x−44x−11
domain x=1 (i.e., (−∞,1)∪(1,∞)).