graph the function f

Question

graph the function f

 

                   2

 

f(x) =  -  1 x  

              5

Answer 1

Any time you are asked to graph a function, it is helpful to identify the parent graph (y=x, y=x², y=(1/x), etc.) Parent graphs are generally graphs that you already know the shape of.  For the function f(x )= -(1/5)x²,

 

a)  the parent graph is...? Graph it.

 

Then look at the function again.  -(1/5)x² tells you how the parent graph has changed.  The + or - sign tells you that the graph is the same shape as the parent graph, or it is the upside-down version of the parent graph.  Since f(x) is negative,

 

b)  is the graph the same shape as the parent graph, or the upside-down version of the parent graph?

 

Look again at the function.  The leading coefficient tells you that the graph is either narrower than the parent graph, the same size and the parent graph, or wider than the parent graph.  Remember that leading coefficients between 0 and 1 make the graph wider than the parent graph.  Leading coefficients greater than 1 make the graph narrower than the parent graph.  Leading coefficients of 1 make the graph the same size as the parent graph.  For the function f(x) = -(1/5)x^2,

 

c)  is the leading coefficient between 0 and 1, larger than 1, or equal to 1?

 

d)  Based on your answer to part c), is the graph going to be wider, narrower, or the same size as the parent graph?

 

Now put all of these answers together; you should have a good idea of what the graph is going to look like.  To get exact points that are on the graph, pick values for x, and solve for f(x).  Plot the points.

 

Answers:

a)  y = x²,  parabola opening upward with vertex at (0,0)

b)  the negative sign means the graph is upside-down (f(x) = -(1/5)x² is a parabola that opens downward)

c)  (1/5) is between 0 and 1 (ignore the negative sign since that was taken care of in part b))

d)  since (1/5) is between 0 and 1, the graph is going to be wider than the parent graph

 

Answer 2

f(x) = 1/5 x^2

 

x | 0 | ±1_| ±2_| ±3

y | 0 | 1/5 | 4/5 | 9/5

 

Graph the points and draw a smooth curve between them, paying attention to the bottom that should be a curve, not a point, with a horizontal tangent at the vertex.