The family of functions that have the domain of all Real numbers and are made only of straight lines.
linear
y=2x - 3
Vertical stretch by a factor of 2 and translate down 2 units
The set of all x-values or inputs of a function.
DOMAIN
Is it a function? {(2, 3), (4, 5), ( -2, 6)}
YES because every input (x) has exactly one output (y).
Identify the domain and range of the following:
D: -2 < x < 4
R: -3 <= y <= 3
The point at which a graph crosses the x-axis, when the y-coordinate is equal to zero.
x-intercept
f(x)=|x-2|+14
translation right 2 units and up 14 units
The set of all y-values or outputs in a function
RANGE
Is it a function?
X Y
2 4
1 6
2 6
NO; the x-value of 2 has two y-values (4 and 6).
What is the domain and range of the graph?
Domain: 0 <= x < infinity
Range: -2 <= y < infinity
This function family is a piecewise function,
{x<0 is y=-x
{x>=0 is y=x
Absolute Value
y = -1/3x2
reflection across the x-axis and vertical compression by a factor of 3
the ratio of change in dependent variable to change in independent variable
slope
Which one(s) are not functions?
B & D
What is the domain of the following arrow diagram?
{-2,0,1,3}
The form of a linear equation that contains two important pieces of information
slope-intercept form
y=2|x+3|-1
The test to tell if a graphed relation is a function
VERTICAL LINE TEST
Is it a function?
NO; it does not pass the Vertical Line Test, for example, x = -2 has two y-values.
What the domain and range of the following?
D: -2 <= x <= 6 R: -6 <= y <= 2
The strength and direction of the relationship between two variables
correlation
y= -5/2x + 5
reflection across the y-axis, stretch (change slope) by a factor of 5/2, translate up 5 units
A linear function in which the ratio of each input to each output is a constant
direct variation
Give an example of a function that has been translated left 2 units, reflected across the x-axis and stretched by a factor of 2.
*answers will vary*
Identify the domain and range of the following graph.
Range: y=-2
Domain: -infinity < x < infinity