The accompanying table expresses the 2010 federal income tax rate schedule for single taxpayers.

a. Express an individual’s income tax as a function of the taxable income x for 0 ≤ x ≤ 171,850, and draw the graph.

b. The graph in part (a) should consist of four line segments. Compute the slope of each segment. What happens to these slopes as the taxable income increases? Interpret the slopes in practical terms.

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If the Taxable Income Is Over But Not Over 0 $8,375 $8,375 $34,000 $34,000 $82,400 $82,400 $171,850 The Income Tax Is 10% $837.50 +15% $4,681.25 +25% $16,781.25 +28% Of the Amount Over 0 $8,375 $34,000 $82,400