Answer:
B. The function shown on the graph has a smaller rate of change but a higher starting point
Explanation:
Question options obtained from a similar question are;
A. The function shown on the graph has a greater rate of change and a higher starting point
B. The function shown on the graph has a smaller rate of change but a higher starting point
C. The function shown on the graph has a greater rate of change but a lower starting point
The function shown on the graph has a smaller rate of change but a higher starting point
Explanation;
The given function with which the graph is compared is y = 4·x + 2
From the given function, we have;
The rate of change of the function is the coefficient of 'x', therefore, the rate of change of the function = 4
When y = 0, 4·x + 2 = 0,
∴ x = -2/4 = -0.5
The y-intercept is given when x = 0
∴ The y-intercept, y = 4 × 0 + 2 = 2
The starting point of the function, is (0, 2)
From the graph, we have;
The y-intercept = (0, 4)
Therefore, the starting point of the line, the y-intercept, (0, 4), is higher than the starting point of the given function, (0, 2)
The coordinates of two (clear) points on the line in the graph are (0, 4) and (-2, -2)
The rate of change of the line, m = (4 - (-2))/(0 - (-2)) = 3
Therefore, the graph has a lesser rate of change, 3, than the rate of change of the given function, 4
When compared with the given function, 'the function shown on the graph has a smaller rate of change and a higher starting point'.