Choose the function represented by the data. The park board has a template for new parks that is 20
yards wide and 30 yards long. To customize the
template to a specific piece of land, a uniform border is
added around the template. The area of the land, f(x),
where x is the width of the uniform border, in miles, is
shown in the table.
O f(x) = 150x3 + 554
O f(x) = 100x3 + 250x + 354
O f(x) = 4x2 + 700
O f(x) = 4x2 + 100x + 600
х
1
2
3
4
5
704
816
936
1,064
1.200

f(x) = 4x² + 100x + 600 represents the function of the area.

Step-by-step explanation:

We are given that the area of the land is f(x) where x is the width of the uniform border, in miles.

Now, from the functions in the options given, let's try f(1) & f(2)for each of them;

f(1) for 150x³ + 554 is;

150(1³) + 554 = 150 + 554 = 704

For f(2);

150(2³) + 554 = 1200 + 554 = 1754

f(1) = 704 tallies with the given value of 704 but f(2) = 1754 does not tally with the given value of 816, thus, 150x³ + 554 does not represent the function of the area

For f(1) into 100x³ + 250x + 354, it gives;

f(1) = 100(1³) + 250(1) + 354

f(1) = 100 + 250 + 354

f(1) = 350 + 354

f(1) = 704

For f(2);

f(2) = 100(2³) + 250(2) + 354

f(2) = 800 + 500 + 354

f(2) = 1654

f(1) = 704 tallies with the given value of 704 but f(2) = 1654 does not tally with the given value of 816, thus, 100x³ + 250x + 354 does not represent the function of the area.

For f(1) into 4x² + 700:

f(1) = 4(1²) + 700

f(1) = 4 + 700

f(1) = 704

f(2) = 4(2²) + 700

f(2) = 16 + 700

f(2) = 716

f(1) = 704 tallies with the given value of 704 but f(2) = 716 does not tally with the given value of 816, thus, 4x² + 700 does not represent the function of the area.

For f(x) = 4x² + 100x + 600:

f(1) = 4(1²) + 100(1) + 600

f(1) = 4 + 100 + 600

f(1) = 704

f(2) = 4(2²) + 100(2) + 600

f(2) = 16 + 800

f(2) = 816

f(1) = 704 tallies with the given value of 704 and f(2) = 816 also tallies with the given value of 816, thus, 4x² + 100x + 600 represents the function of the area.