Question 1180072
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f(x) is a linear function; the area under the curve on the interval [0,4] is a trapezoid with height 4 and bases of lengths f(0) and f(4).<br>
The area of a trapezoid is the height times the average of the bases.<br>
a. f(x)=-2x+8; f(0)=8, f(4)=0; area = 4(8/2) = 16<br>
b. f(x)=x+2; f(0)=2, f(4)=6; area = 4(8/2) = 16<br>
c. f(x)=3x-2; f(0)=-2, f(4)=10; area = 4(8/2) = 16<br>
d. f(x)=5x-6; f(0)=-6, f(4)=14; area = 4(8/2) = 16<br>
e. f(x)=7x-9; f(0)=-9, f(4)=19; area = 4(10/2) = 20<br>
ANSWER: The area is NOT 16 for choice e.<br>
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Alternative solution....<br>
We want the area to be 16; and we know the height is 4.  That means we need the sum of f(0) and f(4) to be 8.<br>
f(0)+f(4) = (0a+b)+(4a+b) = 4a+2b<br>
a. (a,b)=(-2,8); 4a+2b=-8+16=8
b. (a,b)=(1,2); 4a+2b=4+4=8
c. (a,b)=(3,-2); 4a+2b=12-4=8
d. (a,b)=(5,-6); 4a+2b=20-12=8
e. (a,b)=(7,-9); 4a+2b=28-18=10<br>