Use the vertical line test to determine whether or not a graph represents a function.
If a vertical line is moved across the graph and, at any time, touches the graph at only one point, then the graph is
a function. If the vertical line touches the graph at more than one point, then the graph is not a function.
What is the relationship between the graph of a function and the graph of its derivative?
Graphing the derivative with the function can illustrate how to find these turning points. The
function is increasing exactly where the derivative is positive, and decreasing exactly where the derivative is negative
. On the graph of the derivative find the x-value of the zero to the left of the origin.
What is the relationship between functions and graphs?
A function is a relationship between
quantities
where there is one output for every input. If you have more than one output for a particular input, then the quantities represent a relation. A graph of a relationship can be shown to be a function using the vertical line test.
What do you think is the relationship between the graph of the function and the graph of its inverse?
An inverse relation is
the set of ordered pairs obtained by interchanging the first and second elements of each pair in the original function
. If the graph of a function contains a point (a, b), then the graph of the inverse relation of this function contains the point (b, a).
What is the difference between a graph and a function?
We have spoken about the definition of a function. Simply put, it’s
a rule that transforms one real number into another real number
. A graph is a geometric representation of that rule.
What are the two types of functions?
- One One Function.
- Many to One Function.
- Onto Function.
- One One and Onto Function (Bijection)
- Into Function.
- Constant Function.
- Identity Function.
- Linear Function.
What are the types of function graphs?
Different types of graphs depend on the type of function that is graphed. The eight most commonly used graphs are
linear, power, quadratic, polynomial, rational, exponential, logarithmic, and sinusoidal
. Each has a unique graph that is easy to visually differentiate from the rest.
What is the difference between a function and its derivative?
To see the difference between a function and its derivative on a graph we must return to our intuition of the derivative. The derivative is slope or rate of change. So, when the function
is increasing, the derivative is positive
. When the function is decreasing, the derivative is negative.
Which graph is the function and which is the derivative?
The derivative of a function f(x) is the function whose value at x is f′(x). The graph of a derivative of a function f(x) is related to the
graph
of f(x).
What does the first and second derivative tell you about a graph?
In other words, just as the
first derivative measures the rate at which the original function changes
, the second derivative measures the rate at which the first derivative changes. The second derivative will help us understand how the rate of change of the original function is itself changing.
How do you tell if a graph is a function?
Inspect the graph to see if any vertical line drawn would intersect the curve more than once. If there is any such line, the graph does not represent a function.
If no vertical line can intersect the curve more than once
, the graph does represent a function.
What is the graph of one to one function?
Graph of a one-to-one function If f is a one to one function then no two points (x1,y1),
(x2,y2) have the same y-value
. Therefore no horizontal line cuts the graph of the equation y = f(x) more than once. Horizontal Line test: A graph passes the Horizontal line test if each horizontal line cuts the graph at most once.
What is a inverse graph?
GRAPHS OF INVERSE FUNCTIONS: Inverse functions have
graphs that are reflections over the line y = x and thus have reversed ordered pairs
. Let’s use this characteristic to identify inverse functions by their graphs.
Whats a function and not a function graph?
Use the vertical line test to determine whether or not a graph represents a function. If a vertical line is moved across the graph and, at any time, touches the graph at only one point, then the graph is a function.
If the vertical line touches the graph at more than one point, then
the graph is not a function.
Whats a function and not a function?
A function is a relation between domain and range such that each value in the domain corresponds to only one value in the range.
Relations
that are not functions violate this definition. They feature at least one value in the domain that corresponds to two or more values in the range.
How do you tell if something is a function without graphing?
If a vertical line crosses the relation on the graph only once in all locations, the relation is a function. However, if a vertical line crosses the relation more than once, the relation is not a function. Using the
vertical line test
, all lines except for vertical lines are functions.
