1. ALGEBRA II HONORS/GIFTED - INVERSES
12/7/2018
ALGEBRA II HONORS/GIFTED @
INVERSE RELATIONS and FUNCTIONS

2. We have a computer called the Gizmoraptor that does computations for us.Q 27 5
-13 -3
R=5Q + 2 3 2
11) What are the ordered pairs we just made?
(5, 27), (-3, -13), ( , 3), and (0, 2)

3. Now, just for fun, let’s make the Gizmoraptor go backwards
Now, just for fun, let’s make the Gizmoraptor go backwards. Of course, the equation must change. R Q 27 5
-13 -3 3 2
11) What are the ordered pairs we just made?
(27, 5), (-13, -3), (3, ), and (2, 0)
12) What do you notice about the ordered pairs from the two functions R = 5Q + 2 and ?

4. *Get a sheet of graph paper and draw a Cartesian Coordinate System.
*Draw a figure in the 2nd quadrant and note a few of its ordered pairs.
*Draw the line y = x on your coordinate system. We note this line has special properties.
*Fold your coordinate system using the line y = x as the seam of the fold.
*Trace your figure, then draw it on your coordinate system.
*What do you notice about the ordered pairs of the second figure you drew?

5. Recall the equations from before :
R = 5Q + 2 which becomes f(x) = 5x and
which becomes
1)a) Find f(g(2))
b) Find g(f(2))
c) Find f(g(-3))
d) Find g(f(-3))
e) Find f(g(x))
f) Find g(f(x))

6. PROPERTIES OF INVERSES
The ordered pairs are reversed.
The graphs are reflected about the line
y = x.
3) f(g(x)) = g(f(x)) = x
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7. ALGEBRA II HONORS/GIFTED - INVERSES
12/7/2018
HORIZONTAL LINE TEST : The inverse of a function, f, is also a function if and only if no horizontal line intersects the graph of f no more than once.
EXAMPLES
ONE TO ONE FUNCTION : passes both the horizontal and vertical line tests.

8. Find the inverse.
f(x) = 5x original problem
y = 5x let y be f(x)
x = 5y switch the x’s and the y’s
solve for y
let f-1(x) be y

9. 2) Find each inverse and graph f(x) and f-1(x).
a) f(x) = 3x - 7
b) f(x) = x for x > 2
c) f(x) = log62

10. 3) The population of San Yuan can be modeled by
P = 16,500t0.15 , where t is the number of years since 2000.
a) Find the inverse model that gives the number of years as a function of the population.
Answer :
b) What will be the population of San Yuan in 2018?
Answer : 25,455
c) In what year will the population reach 50,000?
Answer : In the year I can’t wait!