Question

Which statement correctly compares the function shown on this graph with

Answer 1

The given highest power of x in the given function, y = 4·x + 2, is 1,

therefore, the graph of the function is a straight line.

The statement that correctly compares the function shown on the graph

with the function; y = 4·x + 2 is; C. The function shown on the graph has a

smaller rate of change but a higher starting point.

Reasons:

The given function is; y = 4·x + 2

Comparing with the equation for a straight line; y = m·x + c, we have;

The rate of change or slope, m = 4

The y-intercept, starting point, c = 2

Two points on the function shown on the graph are; (0, 4), and (-2, -2)

The slope of the given graph is therefore;

$m = \dfrac{4 - (-2)}{0 - (-2) } = \dfrac{6}{2} = 3$

The rate of change of the graph, m = 3

The equation of the graph is therefore;

y - 4 = 3·(x - 0)

Which gives;

y = 3·x + 4

The y-intercept, starting point of the graph, is therefore, c = 4

Which gives;

The function shown on the graph has a higher starting point but a smaller rate of change than the given function.

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