Graph Problem

Question

Graph the function f (x) =

                                         2x +        if               x ≤ -1

                                      { x²            if              -1<x≤2,   and evaluate f (7), f (-2), f (2), f (0), f (-4)

                                         4-3x        if               x>2

Answer 1

To evaluate f(7), plug in x=7 in the  (4 - 3x)  part of the piecewise function.

 

To evaluate f(-2), plug in x=-2 in the  (2x + )  part of the piecewise function.

 

To evaluate f(2), plug in x=2 in the  x²  part of the piecewise function.

 

 

Do you understand the pattern that is taking place here?

Answer 2

Presumably you could graph the three functions that are part of this piecewise definition.

 

You make a composite graph, taking only that part of the first [which seems to be 2x + ??] from -infinity up to -1,

then over the interval (-1,2] you take a part of the parabola y = x², and lastly you complete your piecewise graph by all of the line y = 4 - 3x, for x > 2.

 

f(7) = 4 - 3(7)      f(-2) = (-2)²    f(2) = 2²   f(0) = 0 f(-4) = whatever you get when you substitute into the top piece's [garbled] expression.