The function given in the image is:

$f(x) = 2^{(x - 4)} + 10$

This is an exponential function where the base is 2 and the exponent is $x - 4$, with a vertical shift of +10.

Key points about the function:

1. Exponential Growth: The function represents exponential growth, since the base of the exponent (2) is greater than 1.
2. Horizontal Shift: The term $x - 4$ means that the graph of the function is shifted 4 units to the right.
3. Vertical Shift: The constant +10 means the graph is shifted 10 units upwards.
4. Asymptote: The horizontal asymptote of this function is $y = 10$, because as $x \to -\infty$, $2^{(x-4)} \to 0$, and the function approaches 10.
5. Intercept: To find the y-intercept, substitute $x = 0$ into the function.

Calculating the y-intercept:

$f(0) = 2^{(0 - 4)} + 10 = 2^{-4} + 10 = \frac{1}{16} + 10 = 10.0625$ So the y-intercept is approximately $10.0625$.

Would you like a detailed graph or further explanation?

5 Related Questions:

1. What are the key characteristics of exponential functions?
2. How do horizontal and vertical shifts affect the graph of a function?
3. What is the domain and range of the function $f(x) = 2^{(x - 4)} + 10$?
4. How would the graph change if the base of the exponent were different (e.g., 3 instead of 2)?
5. How can you find the x-intercept of the function?

Tip:

When graphing exponential functions, always note the horizontal asymptote and the behavior as $x$ increases or decreases to understand how the function grows or decays.