To analyze the function [tex]\(f(x) = a^{(x+h)} + k\)[/tex], it's important to understand the roles of the parameters [tex]\(h\)[/tex] and [tex]\(k\)[/tex].
1. Horizontal Shift ([tex]\(h\)[/tex]):
- The term [tex]\(h\)[/tex] inside the exponent [tex]\( (x+h) \)[/tex] affects the horizontal position of the graph.
- If [tex]\(h\)[/tex] is positive, the graph shifts to the left by [tex]\(h\)[/tex] units.
- If [tex]\(h\)[/tex] is negative, the graph shifts to the right by [tex]\(|h|\)[/tex] units.
2. Vertical Shift ([tex]\(k\)[/tex]):
- The term [tex]\(k\)[/tex] outside the exponent (added to the function) affects the vertical position of the graph.
- If [tex]\(k\)[/tex] is positive, the graph shifts upwards by [tex]\(k\)[/tex] units.
- If [tex]\(k\)[/tex] is negative, the graph shifts downwards by [tex]\(|k|\)[/tex] units.
Given the closeness to vertical and horizontal shifts:
- For the horizontal shift, since the correct answer indicates [tex]\( h < 0 \)[/tex], it means the graph shifts to the right.
- For the vertical shift, since the correct answer indicates [tex]\( k > 0 \)[/tex], it means the graph shifts upwards.
Thus, combining these two observations, the correct interpretation is:
[tex]\[
\boxed{C.\ h < 0\ \text{and}\ k > 0}
\][/tex]
