Ch2 I: Function Notation (Solve for x if f(x) = b)
Name: ___________________________ Per. _____
A1.3.C: Use function notation to evaluate find x if f ( x)  b.
f ( x) means the “function with respect to x” … f ( x) is the y-value
f ( x) does NOT mean f times x
Study Notes:
The input variable (called the independent variable) is x.
The output variable (called the dependent variable) is y or
Since
f ( x)
is equal to
y , you can write functions like
f ( x)
y  3x  2 or f ( x)  3x  2
f ( x)  3x  2 , find x if f ( x)  11
Example #1: For the function
Using a more familiar notation, I could ask to find x if
y  3x  2
Set the y-value in the equation equal to 11 and then solve for x:
Solve using an UNDO table:
Do
UNDO
x
Multiply by 3
Add 2
Divide by 3
Subtract 2
Solve:
Result
3
9
11
3x  2  11
3x  2  11
-2
3x
-2

3
subtract 2
9
3 divide by 3
The solution is x = 3
x  3
y  3x  2
That means that the point x = 3 and y = 11 is a point on the graph of
Practice #1: For the function
f ( x)  5( x  3) , find x if f ( x)  50
Set the y-value in the equation equal to 50 and then solve for x:
Solve using and UNDO table:
Do
UNDO
Solve:
5( x  3)  50
5( x  3)  50
Result
x
Subtract 3
Multiply by 5
The solution is x = __________
That means that the point x = _____ and y = 50 is a point on the graph of
y  5( x  3)
Example #2: For the function
f ( x) 
1 x
 4  , find x if f ( x)  32
2
Solve for x graphically using a graphing calculator
1
x
4   32

Set the y-value in the equation equal to 32 and then solve for x: 2
Put each side of the
equation in your calculator:
Find the point where the two
graphs intersect:
MENU
Analyze Graph
Intersect
1 x
 4
2
f 2 ( x)  32
f1 ( x) 
The solution: :x = 3 and y = 32
is a point on the function
Practice #2: For the function f ( x )  42  x , find x if f ( x )  5
Solve for x graphically using a graphing calculator
Set the y-value in the equation equal to 5 and solve for x:
Put each side of the
equation in your
calculator:
42  x  5
The solution: :x=_____ and y = 5
is a point on the function
f1 ( x)  42  x
f 2 ( x)  5
y  42  x
Practice #3: For the function f ( x)  x  2 x , find x if f ( x)  1
Solve for x graphically using a graphing calculator
Set the y-value in the equation equal to 1 and solve for x using a graphing calculator:
2
x2  2 x  1
f1 ( x)  x 2  2 x
The solution: :x=_____ and y = 1
f 2 ( x)  1
and x=_____ and y = 1
Both solutions are points on the
function
y  x2  2x