The table represents values of a linear function. The equation of a line in the slope intercept form is expressed as
y = mx + c
where
m = slope
c = y intercept
We would find the slope and y intercept. The formula for determining slope is expressed as
m = (y2 - y1)/(x2 - x1)
From the table,
if x1 = - 1, y1 = 1
if x2 = 0, y2 = 2
m = (2 - 1)/(0 - - 1) = 1/(0 + 1) = 1/1 = 1
To find the y intercept, we would substitute m = 1, x = - 1 and y = 1 into the slope intercept equation. We have
1 = 1 * - 1 + c
1 = - 1 + c
c = 1 + 1 = 2
This means that the y coordinate of the y intercept of g(x) is 2
The y coordinate of the y intercept of f(x) is 1
Thus,
A) The y coordinate of the y intercept of f(x) is less than the y coordinate of the y intercept of g(x)
Lookng at the graph of f(x) and table representing g(x), the maximum of f(x) is y = 3 and g(1) = 3
Thus,
B) The maximum of f(x) is equal to g(1)
f(x) has 2 zeros at the points where the lines cut across the x axis. The linear graph of g(x) has only one zero. Thus,
C) The number of zeros of f(x) is greater than the number of zeros of g(x)