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11111nata11111 [884]
3 years ago
7

Find the average rate of change of each function over the interval [0, 2]. Match each representation with its respective average

rate of change.

Mathematics
1 answer:
marishachu [46]3 years ago
8 0
Average rate of change over interval [a,b]: r=[f(b)-f(a)]/(b-a)
In this case the interval is [0,2], then a=0, b=2
r=[f(2)-f(0)]/(2-0)
r=[f(2)-f(0)]/2

1) First function: h(x)
r=[h(2)-h(0)]/2
x=2→h(2)=(2)^2+2(2)-6
h(2)=4+4-6
h(2)=2
x=0→h(0)=(0)^2+2(0)-6
h(0)=0+0-6
h(0)=-6
r=[h(2)-h(0)]/2
r=[2-(-6)]/2
r=(2+6)/2
r=(8)/2
r=4

2) Second function: f(x)
A function, f, has an
x-intercept at (2,0)→x=2, f(2)=0
and a y-intercept at (0,-10)→x=0, f(0)=-10
r=[f(2)-f(0)]/2
r=[0-(-10)]/2
r=(0+10)/2
r=(10)/2
r=5

3) Third function: g(x)
r=[g(2)-g(0)]/2
From the graph:
g(2)=6
g(0)=2
r=(6-2)/2
r=(4)/2
r=2

4) Fourth function: j(x)
r=[j(2)-j(0)]/2
From the table:
x=2→j(2)=-8
x=0→j(0)=4
r=(-8-4)/2
r=(-12)/2
r=-6

Answer:
Pairs
1) h(x)     4
2) f(x)      5
3) g(x)     2
4) j(x)     -6
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Answer:

x = (-27)/11

Step-by-step explanation:

Solve for x:

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Put each term in (-11 x)/54 - 1/2 over the common denominator 54: (-11 x)/54 - 1/2 = (-27)/54 - (11 x)/54:

(-27)/54 - (11 x)/54 = 0

(-27)/54 - (11 x)/54 = (-11 x - 27)/54:

(-11 x - 27)/54 = 0

Multiply both sides of (-11 x - 27)/54 = 0 by 54:

(54 (-11 x - 27))/54 = 54×0

(54 (-11 x - 27))/54 = 54/54×(-11 x - 27) = -11 x - 27:

-11 x - 27 = 54×0

0×54 = 0:

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Add 27 to both sides:

(27 - 27) - 11 x = 27

27 - 27 = 0:

-11 x = 27

Divide both sides of -11 x = 27 by -11:

(-11 x)/(-11) = 27/(-11)

(-11)/(-11) = 1:

x = 27/(-11)

Multiply numerator and denominator of 27/(-11) by -1:

Answer:x = (-27)/11

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Answer:

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Step-by-step explanation:

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