4. consider the function f(x) = x2 + 3x – 4.
(a) factor this polynomial and also complete the square. draw a graph of the function.
label the roots and vertex.
(b) this function is not linear, so the "slope" changes as we change the value. we will
investigate that here. find the slope of the line that connects the points (1, f(1))
and (4, f(4) on the graph of f.
(c) we define a new function 91(2x) which finds the slope of the line between the points
(1, f(1)) and (x, f(x)) on the graph of f. in the last step you calculated gi(4). find
91(2), 91(1.5), 91(1.1), and 91(1.01).
(d) explain why 91(1) is undefined. based on the values you calculated in part (c),
what do you think gı(1) should be? use this value for gı(1) from now on.
(e) find the equation of the line through (1, f(1)) with slope gı(20) and draw it along
with the graph of f. what do you notice about how the line relates to the parabola?
(f) define 93(x) to be the slope of the line through (3, f(3)) and (x, f( again 93(3)
is undefined. imagine going through the steps above to find a logical value for 93(3).
(you do not actually have to do this.) do you think the value of 93(3) would be
larger or smaller than gı(1)? why? what about 9-5(-5)?