Which statement correctly identifies a local minimum of the graphed function?
Over the interval [-1, 0.5], the local minimum is 1
.
What are the intercepts of the graphed function?
The intercepts of a graph are
points at which the graph crosses the axes
. The x-intercept is the point at which the graph crosses the x-axis. At this point, the y-coordinate is zero. The y-intercept is the point at which the graph crosses the y-axis.
What does F 0 represent?
The expression f(0) represents
the y-intercept on the graph of f(x)
. The y-intercept of a graph is the point where the graph crosses the y-axis. This occurs where x is equal to 0.
What is the local maximum over the interval?
Then we can say that a local maximum is the point where:
The height of the function at “a” is greater than (or equal to) the height anywhere else in that interval
. In other words, there is no height greater than f(a). Note: a should be inside the interval, not at one end or the other.
What is the range of the function on the graph?
The domain is all x-values or inputs of a function and the range is
all y-values or outputs of a function
. When looking at a graph, the domain is all the values of the graph from left to right. The range is all the values of the graph from down to up.
What does symmetric graph mean in math?
A symmetric graph is
a graph that is both edge- and vertex-transitive
(Holton and Sheehan 1993, p. 209). … A regular graph that is edge-transitive but not vertex-transitive is called a semisymmetric graph. Neither the graph complement nor the line graph of a symmetric graph is necessarily symmetric.
What does F 1 represent on the graph?
The inverse of the function f
is denoted by f
– 1
(if your browser doesn’t support superscripts, that is looks like f with an exponent of -1) and is pronounced “f inverse”. Although the inverse of a function looks like you’re raising the function to the -1 power, it isn’t.
What does F X mean?
The expression “f (x)” means “
a formula
, named f, has x as its input variable”.
Can local minimum be absolute minimum?
An absolute minimum value is a value where and for any other , . Thus, a global minimum is a local minimum in the case where our interval . Thus, we
cannot have an absolute minimum
but not a local minimum, as our absolute minimum is a local minimum.
What is a local minimum?
A function f has a local minimum or relative minimum at a point xo
if the values f(x) of f for x ‘near’ xo are all greater than f(xo)
. Thus, the graph of f near xo has a trough at xo.
How do you find the domain of a graphed function?
Another way to identify the domain and range of functions is
by using graphs
. Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis. The range is the set of possible output values, which are shown on the y-axis.
What statements are true about functions?
All functions have a dependent variable
. All functions have an independent variable. The range of a function includes its domain. A vertical line is an example of a functional relationship..
What is a local minimum and maximum on a graph?
The graph of a function
y = f(x) has
a local maximum at the point where the graph changes from increasing to decreasing. The graph has a local minimum at the point where the graph changes from decreasing to increasing. …
How do you identify the domain and range of a function?
To find the domain and range, we simply
solve the equation y = f(x) to determine the
values of the independent variable x and obtain the domain. To calculate the range of the function, we simply express x as x=g(y) and then find the domain of g(y).
How do you determine if a function is symmetric?
Algebraically check for symmetry with respect to the x-axis, y axis, and the origin. For a function to be symmetrical about the origin, you
must replace y with (-y) and x with (-x)
and the resulting function must be equal to the original function.
How do you tell if a graph is symmetric about the origin?
Mathwords: Symmetric with Respect to the Origin. Describes a graph that looks the same upside down or right side up. Formally, a graph is symmetric with respect to the origin
if it is unchanged when reflected across both the x-axis and y-axis
.
How do you prove a function is symmetric?
A function can be symmetric about a line. when a function is symmetric about x-axis then,
f(y)=f(−y) f ( y ) = f ( − y )
. when a function is symmetric about y-axis then, f(x)=f(−x) f ( x ) = f ( − x ) .
How do we evaluate a function?
To evaluate a function,
substitute the input (the given number or expression) for the function’s variable (place holder, x). Replace the x with the number or expression
. 1. Given the function f (x) = 3x – 5, find f (4).
Is F 1 a function?
| f – 1 (x) f(x) – 1 | Inverse of the function f f(x) – 1 = 1/f(x) (the Reciprocal) |
|---|
How do you find f 0 of a function?
In general, given the function, f(x), its zeros can be found by setting the function to zero. The values of x that represent the set equation are the zeroes of the function. To find the zeros of a function, find
the values of x where f(x) = 0.
What does FX mean in a text message?
FX means “
Effects
.”
What is the difference between local minimum and absolute minimum?
A function can have two types of minima: local and absolute. An absolute minimum, also called a global minimum, occurs when a point is
lower
than any other point on the function. A local minimum, also called a relative minimum, occurs when a point is lower than the points surrounding it.
What is the maximum or minimum point?
A maximum is a high point
and a minimum is a low point: In a smoothly changing function a maximum or minimum is always where the function flattens out (except for a saddle point).
What is the meaning of maximum and minimum?
Minimum means the least you can do of something. …
Maximum means the most you can have of something
. For example, if the maximum amount of oranges you can juggle is five, you cannot juggle more than five oranges. You can do the maximum or less.
How do you find the local maximum of a function?
To find the local maximum, we must
find where the derivative of the function is equal to 0
. Given that the derivative of the function yields using the power rule . We see the derivative is never zero. However, we are given a closed interval, and so we must proceed to check the endpoints.
What is a minimum graph?
The minimum value of a function is
the place where the graph has a vertex at its lowest point
.
Which explains why the graph is not a function?
Which explains why the graph is not a function? It is not a function
because there are two different y-values for a single x-value
. What is the lowest value of the range of the function shown on the graph? … What is the range of the given function?
How do you tell if a table represents a function?
- Identify the input and output values.
- Check to see if each input value is paired with only one output value. If so, the table represents a function.
What do functions represent?
A function is
a relation between a set of inputs and a set of permissible outputs
, provided that each input is related to exactly one output. An example is the function that relates each real number x to its square x2 . The output of a function f corresponding to an input x is denoted by f(x) (read “f of x“).
What is the rule that maps each domain value to its range value?
A function is the relation that takes the inputs of the domain and output the values in the range. The rule for a function is that for each input there is exactly one output. Mapping of a Function: The oval on the left is the domain of the function f , and the oval
on the
right is the range.
Does the graph show a function explain how you know?
The vertical line test can be used to determine
whether a graph represents a function. … If we can draw any vertical line that intersects a graph more than once, then the graph does not define a function because that x value has more than one output. A function has only one output value for each input value.
