d) Graph the reciprocal function.
1)Graph the original
function y = x2 - 4
2) Use the non-permissible
values to draw the
asymptotes.
3) Determine the invariant points
4)Put the invariant points
and y- intercepts on the
graph and use to sketch
the graph of the
reciprocal
Reciprocals of Quadratic Functions
What are the
asymptote lines?
Locate the invariant
points
7.4
Example 3: Your Turn
2
Answer
Consider f (x) = x + x – 6.
a) What is the reciprocal function of f (x)?
b) State the non-permissible values of x and the equation(s) of the
vertical asymptote(s) of the reciprocal function.
c) What are the x-intercepts and the y-intercept of the reciprocal
function?
d) Sketch the graphs of y = f (x) and its reciprocal function
.
Answer
a) Find the reciprocal of the
point given (y - value)
The x intercept must be at the
asymptote so that is the
second point
Use the two points to find the
equation of the line
b) Use the equation of the line to find the original function.
7.4
Example 4: Your Turn
The graph of a reciprocal function of the form
a
Answer
where a and b are non-zero constants, is shown.
a) Sketch the graph of the original function, y = f (x).
b) Determine the original function y = f (x).
!"#$%&'()*'$y = f ( x) !"##$#%&'()*+'%!),-&%./0%12345%
6'$%($7,!()7"8%)9%&',#%9*-7:)-%'"#%"%;$(:7"8%"#<=!&)&$%
"&%>%?%@5%A("!'%&'$%9*-7:)-%"-B%,&#%($7,!()7"8%"-B%C(,&$%
D)&'%$E*":)-#%($!($#$-&$B%D<%&'$%+("!'#5
f(x) = | 1/3 x ! 5 |
y=|!3 x2 +2 x+2|
f(x) = |-4x - 5 |
y=|1/2 x2 !3 x + 2|
Graph y = 5x - 2 and its reciprocal:
V. A: 5x-2=0
x=2/5
H.A: y = 0
Invariant Pts:
Questions on pages 324 - 330
of your workbook.