Increasing and Decreasing Graphs

1
Increasing and Decreasing Graphs

• By Naiya Kapadia,YiQi Lu, Elizabeth Tran

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Linear Function

• - Increasing and decreasing lines are determined
  by the graph's slope, which can be found in the
  linear equation form, y mxb.

• 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."

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
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Quadratic Function

• -

A quadratic function has the form y ax2 bx
c , where "a" cannot equal 0.
Increasing Graph

• To tell whether the graph is an increasing
  function, a gt 0 and the graph opens upward. This
  causes the "x" term of the graph to be positive ,
  as shown in the "increasing graph."

Decreasing Graph

• To tell whether the graph is a decreasing
  function, a lt 0 and the graph opens downward.
  This causes the "x" term of the graph to be
  negative, as shown in the "decreasing graph."

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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."

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Exponential Function

• Decreasing
• y abx is an exponential decay function when a
  gt 0 and 0 lt b lt 1, which is a decreasing
  function.
• With an exponential decay graph, the graph would
  be a curve line that decreases from the top of
  left down to the right, which is a curve line of
  decreasing
• y a(1-r)t can use for a real-life quatity
  decreases by a fixed percent each year.

• Increasing
• y abx is an exponential growth function when
  a gt 0 and b gt 1, which is an increasing function.
• This is a graph of exponential growth
  function,the graph has a curving line that is
  going from the bottom of left up to right, that
  is an increasing line.
• To apply the exponential growth function into
  real life, you can use y a(1r)t for a real
  life quantity increases by a fixed percent each
  year.

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Radical Function

• -y avX and y a 3vX (3vX is a cubic root) are
  radical functions.
• - If a gt 1, then it would be an increasing
• function for both y avX and y a 3vX
• 
  
• 
  y a 3vX
  y avX
• - If a lt 1, then it would be a decreasing
• function for both y -avX and y -a 3vX
• 
  y -a 3vX
  y -avX

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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 lt b lt 1. The
• 
  graph moves down to the right.
• a decreasing graph

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Absolute Value
Increasing graph

• - Put into the form of yax-hk
• -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
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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.
• - 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 domain can change that. Look at
  example.

Example of a piecewise function
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.