Transcript Increasing and Decreasing Graphs

Increasing and
Decreasing Graphs
By: Naiya Kapadia,YiQi Lu,
Elizabeth Tran
Linear Function
- Increasing and decreasing lines are determined by the graph's slope, which
can be found in the linear equation form, y= mx+b.
Increasing Graph:
•
To tell whether the graph is an increasing
function, the slope must be positive, and
the graph runs from left to right, as shown
in the "increasing graph."
Decreasing Graph:
•
To tell whether the graph is a decreasing
function,the slope must be negative, and the
graph runs from right to left, as shown in the
"decreasing graph."
y= -1/4
Quadratic Function
-
A quadratic function has the form y= ax^2 + bx + c , where "a" cannot
equal 0.
Increasing Graph:
•
•
To tell whether the graph is an
increasing function, a > 0 and the graph
opens upward. This causes the "x" term
of the graph to be positive , as shown in
the "increasing graph."
To tell whether the graph is a
decreasing function, a < 0 and the
graph opens downward. This causes
the "x" term of the graph to be negative,
as shown in the "decreasing graph."
Decreasing Graph:
Correlation
- Also known as the "best fitting lines", correlation helps show the linear
relationship of (a) set(s) of data.
•
To tell whether a correlation graph is
increasing, the slope must be positive,
gradually progressing from the bottom left to
the top right of the grid, such as the example
of the "increasing graph."
Decreasing Graph:
Increasing Graph:
•
To tell whether a correlation graph is increasing, the
slope must be negative, gradually progressing from
the top left to the bottom right of the grid, such as
the example of the "decreasing graph."
Exponential Function
Increasing
Decreasing
y = ab^x is an exponential growth
function when a > 0 and b > 1, which is
an increasing function.
y = ab^x is an exponential decay
function when a > 0 and 0 < b < 1,
which is a decreasing function.
This is a graph of exponential growth
function,the graph has a curving line
that is going from the bottom of left
With an exponential decay graph, the
graph would be a curve line that
decreases from the top of left down
Radical Function
-y = a√X and y = a 3√X (3√X is a cubic root) are radical functions.
- If a > 1, then it would be an increasing
function for both y = a√X and y = a 3√X
y = a 3√X
- If a < 1, then it would be a decreasing
function for both y = -a√X and y = -a 3√X
y = a√X
Logarithmic Function Graph
-Logarithmic Functions: y = logb(x - h) + k
~ For a logarithmic function to increase,
the "b" value must be greater than 1.
The graph is moving up to the right.
an increasing graph
~ A decreasing logarithmic function
has a "b" value that is 0 < b < 1. The
Absolute Value
Increasing graph
- Put into the form of y=a|x-h|+k
-The "a" value is almost like the
slope. It can be either positive
or negative.
- If the "a" value is positive, the
graph opens upwards as shown
in the "increasing graph".
-If the "a" value is negative, the
graph opens downwards as
shown in the "decreasing graph".
Decreasing graph
Piecewise Function
Example of a piecewise function:
- A function represented by a
combination of equations, each
corresponding to a part of the
domain.
- The equations can be linear,
quadratic, polynomial...etc., as
long as they have x-value
constraints.
Notice that the slope of the first
equation is positive, but the graph is
going down. This is because the
constraint is making the graph look like
it's decreasing from that point of -3.
The second equation is a negative and
stays negative even after the
constraint.
- The equation of the original graph
tells you if the graph is
decreasing or increasing or
doing both at certain points on
the graph. The slope is what
determines this aspect of the
graph, but the constraint of the