The table below gives the values of two functions, g and h, for various values of x.
One of the functions expresses a relationship that can be expressed by the formula
a + bx, where a and b are real number coefficients.
What is the value of that function for x = 0?
x........g(x)....h(x)
-3.......4
-2.......2...........3
-1.......1...........6
0
1........1
2...................15
3...................18
?
Favorite Answer
The answer is 9 because g(x) is a parabola, not a linear function of the form ax + b.
You can tell because as x increases from -3 to -2, g(x) decreases by 2,
then when x increases from -2 to -1, f(x) decreases by 1.
This is not linear behavior. Also, f(-1) and f(1) are both = 1.
Straight lines do not decrease and then increase again.
However, these values fit the description of a parabola very well.
Thus f(x) must be the linear function, and from the values
you see that f(x) increases by 3, as x increases by 1.
Thus f(0) = f(-1) + 3 = 6 + 3 = 9
Maggie C
Test for the slope: (y2-y1)/(x2-x1)
For g(x): (2-4)/(-2-(-3)) = -2 but using the next two points (1-2)/(-1-(-2)) = -1 so the lines connecting the two points are not the same.
For h(x): (6-3)/(-1-(-2)) = 3 and (18-15)/(3-2) = 3 so the slope of the line is 3.
Using y-y1 = m(x-x1)
y-3 = 3(x-(-2))
y-3 = 3x + 6
y = 3x + 9
so h(x) =3x + 9 and h(0) = 9