Functions

Question 1

Function (main definition)

Answer 1

Presented as f that is a rule assigned to each value (x) in a set D which is a unique value denoted to f(x).

Question 2

Set D (main definition)

Answer 2

The domain of the function.

Question 3

Range (main definition)

Answer 3

Set of all values of f(x) produced as x varies over the entire domain.

Question 4

Two y values for one value of x

Answer 4

Fails test-not a function

Question 5

Two times for one temperature

Answer 5

A function

Question 6

Vertical Line Test (main definition)

Answer 6

-A graph that represents a function and if only it passes the vertical line test.
-A vertical line intersects the graph at most once.

Question 7

Composite Functions (main definition)

Answer 7

Given two functions f and g (f o g) is defined by ( f o g)(x)=f(g(x)).
-Function g —> u=g(x) —> Function f —> y=f(u)=f(g(x))

Evaluated into two steps:
y=f(u), where u=g(x). The domain of f o g consists of all x in the domain of g such that u=g(x) is in the domain of f.

Question 8

Symmetry in Graphs (y-axis, x-axis, and origin)

Answer 8

Symmetric to y-axis: Whenever the point (x,y) is on the graph, the point (-x,y) is also on the graph. Property of graph is unchanged when reflected across the y axis)

Symmetric to x-axis: Point 9x,y) is on the graph, the point (x,-y) is on the graph as well. Meaning the property of the graph is unchanged when reflected across the x-axis)

Symmetric to origin: Point (x,y) is on the graph, point (-x,-y) is also on the graph. meaning both x and y axes implies symmetry about the origin, but not vice versa.

Question 9

Symmetry in Functions (even and odd)

Answer 9

Even: f has the property of f(-x)=f(x) for all x in the domain. The graph of the even function is symmetric about the y-axis.

Odd: f has the property of f(-x)=-f(x), for all x in the domain. The graph of the odd function is symmetric about the origin.