Question

Which table will have the greatest value of y when x = 7?
x y(a)
-1 3
0 0
1 3
2 12
3 27


x y (b)
-1 -10
0 2
1 14
2 26
3 38

x y (c)
-1 0.5
0 1
1 2
2 4
3 8

x y (d)
-1 -8
0 2
1 12
2 22
3 32

Answer 1

Answer:

(a) (x, y) = (7, 147)

Step-by-step explanation:

Table A represents a quadratic function: y = 3x², so for x=7, y = 3·7² = 147.

Table B represents a linear function: y = 12x +2, so for x=7, y = 86.

Table C represents an exponential function: y = 2^x, so for x=7, y = 128.

Table D represents a linear function: y = 10x +2, so for x=7, y = 72.

The greatest value of y for x=7 will be found in Table A.

_____

Table a's values go down and up, with symmetry about x=0. This suggests a quadratic function. A plain y=x² function will have the value 1 at x=1. This one has the value 3, so looks like y = 3x². Checking values for x=2 and x=3 confirms this.

Table b's values go consistently up, with a difference of 12 each time. The value for x=0 is 2, so we know this linear function has equation y=12x+2.

Table c's values double from one value of x to the next, so the function is exponential with a base of 2. The multiplier is 1, the value for x=0, so the equation is y = 1·2^x.

Table d is similar to table b, except the common difference is 10 instead of 12. So, the slope in slope-intercept form is 10 instead of 12: y = 10x + 2.

Answer 2

The table with the highest value of y when x = 7,

is table A!

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