Question

1. sketch a graph of a function with the given characteristics.

• the x - intercepts are - 7/2, - 1/2, and 5/2.
• the function is increasing when x < - 3/2, decreasing when - 3/2 < x < 1, and increasing when x > 1.

Explanation:

Step1: Plot x - intercepts

Mark the points \((-\frac{7}{2},0)\), \((-\frac{1}{2},0)\), and \((\frac{5}{2},0)\) on the x - axis.

Step2: Analyze increasing/decreasing intervals

• For \(x<-\frac{3}{2}\), the function is increasing. So, draw the graph rising to the left of \(x =-\frac{3}{2}\).
• For \(-\frac{3}{2}
• For \(x>1\), the function is increasing. So, draw the graph rising to the right of \(x = 1\).

Answer:

A graph with x - intercepts at \((-\frac{7}{2},0)\), \((-\frac{1}{2},0)\), \((\frac{5}{2},0)\), increasing for \(x<-\frac{3}{2}\) and \(x > 1\), and decreasing for \(-\frac{3}{2}