Lesson 1- Functions Flashcards
What is a relation?
A set of ordered pairs.
Define: Domain
The set of first co-ordinates of a relation (R).
Define: Range
The set of second co-ordinates of a relation (R).
What are four ways to represent a relation?
Equation
Graph
Set of ordered pairs
Table of values
Determine the domain: (0,0) (1,1) (4,2) (9,3) (16,4)
0, 1, 4, 9, 16
Determine the domain and range of y = 2x + 1 .
Domain: all real numbers
Range: all real numbers
When reading inequalities, we always read from the ___ to the ___.
Variable to the number
Read the following inequality: 7 <_ x
x is greater than, or equal to 7.
Determine the range of the following graph:
Range: -4 <_ y < 7
Determine the domain of the following graph:
Domain: -3 <_ x <_ 8
What is the domain of this graph?
Domain: -5 <_ x <_ 7
What is the range of this graph?
Range: (-3. -1, 1, 3)
What is the basic definition of a function?
For every input value, there is only one output value.
Performs an operation on an input value and gives an output value.
What is the formal definition of a function?
Does this graph represent a function?
No, the graph produces 2 y values for one x value.
Does this graph represent a function?
No, the graph produces two y values for one x value.
How can we determine if an equation is a function?
1- Solving for y to see if a unique y-value is produced.
2- Checking by substituting x- values (must produce only one y-value)
Is y^2 = x a function?
Is x^2 + y^2 = 16 a function ?
(hint: solve for y)
No, when solving for y:
y= +- /16 - x^2
A unique y-value is not produced.
Is this a function: (2,6) (3,9) (6,21) (8,43) ?
Yes, each x value produces a unique y-value.
Is x = /y a function?
Yes, when solving for y:
y = x^2
Is x2 = 9 - y2 a function?
No, when solving for y:
y= +_ /9-x2
How do we determine the domain of a radical function?
Make the radicand greater than, or equal to 0.
How do we determine the domain of a rational function?
Make the denominator not equal to 0.
What is the domain of y = /x+2 ?
x + 2 >_ 0
x >_ -2
How do we find the range of y = /x+2 ?
Substitute the -2 from the domain into the radicand.
y= /-2 + 2 y = 0
y >_ 0
What is the domain of y= /5-x - 4 ?
5 = x >_ 0
-x >_ -5
x
What is the range of y = /5-x - 4 ?
y= /5-5 - 4 = 0 - 4 = -4
y >_ -4
What is the domain of y = 1/ x+4 ?
What is the range of y = 1/x+4 ?
y =/ 0
(substitute -4 in the denominator from the domain)
What is the range of y= -4x2 - 1 ?
By substituting x values, we see that y values must be:
y
What kind of function is this?
y = 0x + 1
What kind of function is this?
2y + 3x = -6
The linear function.
What kind of function is this?
y = x2
Produces a parabola with an axis of symmetry and vertex.
The quadratic function.
What kind of function is this?
y = x3
Domain all real numbers, range all real numbers
The cubic function.
What kind of function is this?
y = 1/x
Has an asymptote.
The reciprocal function.
What kind of function is this?
y = {x}
Produces a v- shaped graph;
The absolute value function.
What kind of function is this?
The square root function
What kind of function is this?
y= /16-x2
x2 + y2 = 16 (radius 4)
The semicircle function.
List the eight major types of functions.
Constant function
Linear function
Quadratic function
Cubic function
Reciprocal function
Absolute value function
Square root function
Semicircle function
