(e) What type of function always increases at the same rate? What do we call its rate ofincrease?3. Sketch the functiony=x2+ 1and use it as directed below.(a) Draw the line between the points on the curve atx= 1andx= 2. What is its slope?(b) Draw the line between the points on the curve atx= 1andx= 1.3. What is its slope?(c) Draw what you imagine would be the tangent line to the curve atx= 1(touches thecurve at just that point)(d) What seems to happen as you draw lines between the pointx= 1and points approach-ingx= 1? (sayx= 1.1,x= 1.01, etc.)

4. As a certain object falls, its positions(in meters) above ground aftertseconds is given bys(t) = 20-5t2.(a) What is the average velocity of the object on the interval fromt= 1to the time0.5seconds later?(b) What is the average velocity of the object on the interval fromt= 1to the time0.1seconds later?(c) Write a polynomial in terms ofhfor the average velocity fromt= 1to the timehsecondslater (h6= 0).(d) What does this average tend toward forhcloser and closer to0(smaller and smallertime interval)?(e) What would you guess to be the exact velocity of the object after1second?5. Draw the graph of the functiony=f(x) = 1/xbetweenx= 1/2andx= 4. Find the slopeof the line between the points (a)x= 3andx= 3.1, (b)x= 3andx= 3.01, (c)x= 3andx= 3.001. Now use algebra to find a simplified rational expression for the slope of the linebetween(3, f(3))and(3 +h, f(3 +h)),(h6= 0). What do these slopes tend toward ashismade closer and closer to 0.——————————————————————-