Question

Use the three representations below to answer questions 3 & 4.

3) Which function has the greatest rate of change?

4) Which function has the greatest initial value?​

Answer 1

3) The function that has the greatest rate of change or slope is Function A.

4) The function that has the greatest initial value is Function B.

Using the slope of the line tangent to the curve at a given point, we can determine the rate of change or slope of each function as follows:

The slope of a line is given by the formula:

slope = (change in y) / (change in x)

For Function A, the slope of the tangent line at any point is 4 {(10 - 2)/4}

For Function B, the slope of the tangent line at any point is 2.5 (5/2)

For Function C, the slope of the tangent line at any point is -1.

Thus, Function A has the greatest rate of change.

The initial value of each function is the y-intercept of the line.

For Function A, the y-intercept is 2.

For Function B, the y-intercept is 3.

For Function C, the y-intercept is 0.

Thus, Function B has the greatest initial value.