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•All exponential graphs take this shape, but they can be shifted, turned upside down or stretched.
•All exponential graphs take this shape, but they can be shifted, turned upside down or stretched.
•Changing the base number (p) will change the shape of the curve. For this year most of your base numbers will be 2.
•Changing the base number (p) will change the shape of the curve. For this year most of your base numbers will be 2.
•A key feature of an exponential is the asymptote - a line they get very close to but never touch.
•A key feature of an exponential is the asymptote - a line they get very close to but never touch.
In this equation, you can see that the equation gets very close to zero but in reality it never actually reaches zero. Meaning that zero is the asymptote
Vertical Shift
Vertical Shift
- To move an exponential up/down we add/subtract to the end of the equation.
- This shifts the asymptote up and down
For this equation the asymptote shown on the graph is 2
For this equation the asymptote shown on the graph is 2
Horizontal Shift
Horizontal Shift
- To move a exponential right ‘b’ units we subtract from the x
- The key point to look at is always one above the asymptote to see how it has shifted.
The standard
Can see key point has shifted left two
Can see key point has shifted right one
The idea around the transformations of exponentials is similar to that of the quadratics for vertical and horizontal shifts.
The idea around the transformations of exponentials is similar to that of the quadratics for vertical and horizontal shifts.
The different is that we are looking at the point one above an asymptote in exponentials, compared to the vertex in quadratics.
🠔 Click on the image to see how exponential transformations work
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