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Graphs! :pencil2: (Exponential Graphs y=a^x (y= e^x (image
If x is…
Graphs! :pencil2:
Exponential Graphs y=a^x
The remarkable thing about exponential is that they all have a y-intercept of 1! ... unless transformed...
As x decreases the graph tends towards 0 (asymptote).
whenever a is between 1 and 0, the graph is a decreasing function which means that the graph tends towards zero as x increases. We say as x increases, y decreases.
Hint! The graph of y= (1/a)^x is the reflection of y=a^x in the y axis.
Remember, the graph of y=(1)^x is just a straight line!
y= e^x
The graph of y =e^x follows similar trends, the y intercept is also 1 (unless translated) and the smaller the value of the constant, the steeper the graph is and the closer it is to the x -axis.
If x is negative the graph has a decreasing function, so as x increases, y decreases!
Here's what the graph will look like if the constant is negative!
x --> ∞, y --> - ∞
x--> -∞, y --> 4
Hint! When the graph is transformed, let =0, and solve to find the y-intercept.
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Cubic Graphs
When x --> ∞, y --> ∞
x--> -∞, y --> -∞
Draw the cubic graph from the bottom left side corner to the top right hand corner.
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When a >1 the function increases
When 0 > a < 1 the function decreases
A negative x value will flip the graph about the y -axis.
A negative value for a will flip the graph about the x -axis.