Question 1 (1 point)
Given the function $y=(2.5)^{x}-6$ what is the equation of the horizontal asymptote?
a) $y=0$
b) $y=2.5$
c) $y=-6$
d) $y=-3.5$

Step 1 ：Given the function \(y=(2.5)^{x}-6\), we need to find the equation of the horizontal asymptote.

Step 2 ：The horizontal asymptote of a function is the value that the function approaches as x approaches infinity or negative infinity.

Step 3 ：For the given function \(y=(2.5)^{x}-6\), as x approaches infinity, the term \((2.5)^{x}\) will also approach infinity. However, the term -6 is a constant and does not change with x. Therefore, the function will approach infinity minus a constant as x approaches infinity, which is still infinity.

Step 4 ：As x approaches negative infinity, the term \((2.5)^{x}\) will approach 0, because any positive number to the power of negative infinity is 0. Therefore, the function will approach 0 minus a constant as x approaches negative infinity, which is -6.

Step 5 ：So, the horizontal asymptote of the function is \(y=-6\).

Step 6 ：Final Answer: The equation of the horizontal asymptote is \(\boxed{y=-6}\).