Part A: Exponential Function with Transformations

a) State your Parent Base Function (Knowledge: 1 mark):

The parent function for an exponential function of base 10 is:

$f(x) = 10^x$

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b) State your Transformed Function (Knowledge: 1 mark):

A transformed function with at least 5 transformations can be written as:

$g(x) = -2 \cdot 10^{(x-3)} + 5$

Explanation of Transformations:

1. Vertical Reflection: The negative sign (-) reflects the graph across the x-axis.
2. Vertical Stretch: The coefficient 2 stretches the graph vertically by a factor of 2.
3. Horizontal Shift: The term (x - 3) shifts the graph 3 units to the right.
4. Vertical Shift: The +5 shifts the graph 5 units up.
5. Base Retention: The base 10 remains unchanged, preserving the exponential nature.

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Would you like detailed graphs or further explanations for these transformations? Let me know!

Five Related Questions:

1. How does a vertical stretch or compression affect the graph of an exponential function?
2. What is the significance of the horizontal shift in the function $(x-h)$?
3. How does changing the base of an exponential function impact its growth rate?
4. Can you identify the y-intercept of the transformed function $g(x)$?
5. How would a horizontal compression be introduced into this function?

Tip:

Always write your transformations step by step to clearly identify the sequence and their combined effects on the graph!