The question asks you to describe the function $g(x)$ in terms of $f(x)$, given that the transformation involves a vertical stretch, a horizontal shift to the right, and a vertical shift upwards.

Transformation details:

1. Vertical stretch: By a factor of 2, so the term outside of $f(x)$ will be 2.
2. Horizontal shift: To the right by 8 units, so we replace $x$ by $(x - 8)$.
3. Vertical shift: Upward by 7 units, so we add 7 to the function.

The general form for a transformed function is: $g(x) = A f(x + B) + C$ We will now plug in the values based on the transformations.

• $A = 2$ (vertical stretch by a factor of 2),
• $B = -8$ (since a shift to the right by 8 is represented as $(x - 8)$),
• $C = 7$ (shift upward by 7 units).

Thus, the function is: $g(x) = 2 f(x - 8) + 7$

Therefore, the values are:

• $A = 2$
• $B = -8$
• $C = 7$

Let me know if you want more details or have any questions!

5 Related Questions:

1. How would the equation change if the function was shifted left instead of right?
2. What if the vertical shift was downwards instead of upwards?
3. How does a horizontal compression affect the equation?
4. How would a reflection over the x-axis impact the function?
5. What if the vertical stretch factor was different, say 3 instead of 2?

Tip:

When transforming functions, always remember that horizontal shifts affect the inside of the function (with opposite signs), while vertical shifts affect the outside directly.