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UNIT 4 LESSON 5
NOTES 2
Solving f(x) = g(x) Algebraically
EXAMPLE:
 Barbara
has a bunny that weighs 5 pounds and
gains 3 pounds per year. Her cat weighs 19
pounds and gains 1 pound per year. When will
the bunny and the cat weigh the same amount?


If x is the number of years and y is the weight, write
an equation that represents the bunny’s weight (y)
after a given number of years (x).
Bunny: y = 3x + 5
 Barbara
has a bunny that weighs 5 pounds and
gains 3 pounds per year. Her cat weighs 19
pounds and gains 1 pound per year. When will
the bunny and the cat weigh the same amount?


If x is the number of years and y is the weight, write
an equation that represents the cat’s weight (y) after a
given number of years (x).
Cat: y = 1x + 19

When two equations are equal to the same thing
(or variable) then you can put them equal to each
other and solve.
Bunny: y = 3x + 5
3x + 5 = x + 19
-1x
-x
2x + 5 = 19
-5 -5
2x
= 14
x
= 7
Cat:
y = x + 19
The Bunny and
Cat’s weight will
be equal after 7
years.
SOLVING F(X) = G(X)
ALGEBRAICALLY
Replace any function notation
f(x), g(x), with y =
Place the two functions equal to each other.
Looking at what type of function you have,
solve the equation using appropriate
method.
SOLVING DIFFERENT TYPES OF EQUATIONS
Linear:
1. Get x to one
side of equal
sign.
2. If a constant is
with x,
add/subtract
that value to
both sides.
3. If a number is
being
multiplied by x,
divide both
sides by that
number.
Quadratic:
1. If there is an x2
and NO x term,
get x2 by itself
and take square
root of both
sides.
2. If there is an x2
AND an x term,
get one side
equal to zero,
factor , put equal
to zero and then
solve for x.
Absolute Value:
1. Get |x| by
itself on one
side of equal
sign.
2. Make two
equations and
set equal to
positive
answer AND
negative
answer.
3. Solve for x.
EXAMPLE 1:
FIND THE SOLUTION TO F(X) = G(X).
f(x) = 7x – 3
and
g(x) = x + 15
(same as y = 7x – 3 and y = x + 15)
Both are linear
functions
7x – 3 = x + 17
6x – 3 = 15
6x = 18
x=3
EXAMPLE 2:
FIND THE SOLUTION TO F(X) = G(X).
f(x) = x2 – 4
Quadratic but NO
‘x’ term
and g(x) = 45
x2 – 4 = 45
x2 = 49
x = 7 and -7
EXAMPLE 3:
FIND THE SOLUTION TO F(X) = G(X).
f(x) = x2 – 5x
Quadratic - with x2
AND ‘x’ term
and
g(x) = 2x – 10
x2 – 5x = 2x – 10
x2 – 7x + 10 = 0
(x – 5)(x – 2) = 0
x = 5 and x = 2
EXAMPLE 4:
FIND THE SOLUTION TO F(X) = G(X).
f(x) = |x – 19| and
g(x) = 22
|x – 19| = 22
Absolute Value
Function
x – 19 = 22
x – 19 = -22
x = 41 and
x = -3