Let's figure some information for each function first.
Function A
The rate of change is the change in y divided by the change in x. Let's take the first 2 pair of points.
The change in y is 7 - 3 = 4
The change in x is 2 - 1 = 1
The rate of change is 4/1 = 4
The y-intercept is the y-axis cutting point. It occurs at x = 0. The functional table doesn't have x = 0.
Since were were adding 4 for each increase in x, we should be subtracting 4 for each decrease of x. Thus, from x = 1 to x = 0, the y would be 3 - 4 = -1
The y-intercept is - 1
Function B
The rate of change of a linear graph is the change in y coordinates divided by the change in x coordinates when we move from one point on the line to another.
One poin tis (0, -3) and another point is (3, 0). Thus, the rate of change would be:
[0 - -3]/[3 - 0] = 3/3 = 1
The rate of change is 1
The y-intercept is clearly seen from the graph, it is -3
The y-intercept is -3
Now, let's check the statements and write TRUE or FALSE.
Statement 1:
The rate of change of both function is positive. TRUE.
since rate of change of both functions are 4 and 1 , respectively.
Statement 2:
Rate of change of A is 3 times Rate of change of B. FALSE.
because they are 4 and 1 , which means the rate of change of A is "4" times (not 3 times) that of Function B.
Statement 3:
The y-intercepts of both functions are positive. FALSE.
The y intercept of first function is -1 and of the second function is -3. Thus, they are both negatives, not positives.