Math 205 - Calculus 1
Homework due September 9
Question 1. Recall that the function f(x) = |x|has a V-shaped graph with its cusp (corner point)
at the origin (0,0) with the cusp pointing down.
(a) Manipulate f(x) = |x|so that its cusp now occurs at (โ2,4) instead of the origin and that
the cusp is still pointing down. Write down your manipulated function and graph it.
(b) Manipulate f(x) = |x|so that its cusp now occurs at (1,โ3) instead of the origin and that
the cusp is now pointing up. Write down your manipulated function and graph it.
Question 2. Assume that f(x) is a function with domain (โโ,2] and range [โ4,1). What is the
domain and range of its inverse fโ1(x)? Explain why your answer makes sense.
Question 3. Consider the linear function f(x) = โ3x+ 2.
(a) Graph f(x) by plotting some sample points.
(b) Graph fโ1(x) by plotting sample points, which you get by reversing the inputs and outputs
of f(x).
(c) Verify that your graph of fโ1(x) is the graph of f(x) reflected about the diagonal line y=x.
(d) Given that y=โ3x+ 2, find the equation for the inverse by switching xand yand solving
for the new y.
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