Day 1 Notes: Functions Review
Absolute Value: The distance (# of units) from zero.
Examples:
2 2
5 5
Function Notation:
 y  2 x  5 is equivalent to f  x   2 x  5
 the function notation is read “f of x equals 2x + 5” or “find the value
of the function (y) when x is given”
 Example: Given f  x   2 x  5 , find f 3
Function: A relation is a function if each x-value has only one
corresponding y-value.
Example:
Function: Note that the relation above
passes the vertical line test; a vertical
line will cut the curve at only one point
anywhere on the curve.
Example:
Not a Function: Note that the relation
above does not pass the vertical line test.
x  y2
x   y2
y  x2
x
y
-2
4
-1
1
1
1
2
4
Note: each x-value has only 1
corresponding y-value
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x  y
y x
x
y
1
1
4
2
Note: each x-value has more than 1
corresponding y-value
x and y intercepts: where the curve crosses the x and y axes respectively
x-intercept: where the curve
crosses the x-axis
Note: y = 0
y-intercept: where the curve
crosses the y-axis
Note: x = 0
Example: Given x  2 y  2 , find the x and y intercepts
Graph to confirm:
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Restrictions: values for which an expression or a relation are undefined
Examples: State the value(s) of x for which the following expressions are
undefined:
1
2x
3
a)
b)
c) 2
d) x  6
x3
x5
x  2x
Domain and Range:
Domain: the set of x-values for a relation
Range: the set of y-values for a relation
Examples: Determine domain and range for each of the following (hint:
determine any restrictions) Write in set notation and interval notation.
a)
y  x2
b) y  x  3
-3
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A special Note:
a) evaluate
25
b) solve for x, if x 2  25
Review Basic Functions:
Linear:
y  mx  b
Domain: reals
Range: reals
Identity: y  x
Constants:
ya
a
Domain: reals
Range: y  a
xa
Domain: x  a
Range: reals
Quadratic: graphs a parabola
y  x2
Domain: reals
Range: y  0
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x
-2
-1
0
1
2
y
4
1
0
1
4
a
Absolute Value:
y x
Domain: reals
Range: y  0
Cubic:
y  x3
Domain: reals
Range: reals
Square Root:
y x
Domain: x  0
Range: y  0
x
0
1
4
9
y
0
1
2
3
Reciprocal: graphs a hyperbola
1
x
Domain: x  0
Range: y  0
y
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x
-2
-1
-0.5
0.5
1
2
y
-0.5
-1
-2
2
1
0.5
x
-2
-1
0
1
2
y
2
1
0
1
2
x
-2
-1
0
1
2
y
-8
-1
0
1
8