Yes, $h(x) = 2^x - 6$ is an exponential function.

An exponential function has the form $f(x) = a \cdot b^x + c$, where:

• $a$ is a constant,
• $b$ is the base of the exponential, and
• $x$ is the exponent.

In your case:

• The base $b = 2$,
• The exponent is $x$,
• The constant shift is $-6$, which just translates the function vertically.

Since the variable $x$ is in the exponent and the base is a constant (2), it classifies as an exponential function. The term $-6$ affects the vertical position of the graph but does not change the exponential nature of the function.

Would you like a detailed breakdown of how to graph this function or further explanation?

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Here are some related questions:

1. How does the vertical shift affect the graph of an exponential function?
2. What is the significance of the base in an exponential function?
3. How do you find the asymptote of the function $h(x) = 2^x - 6$?
4. Can the base of an exponential function be negative? Why or why not?
5. How does the function $h(x) = 2^x - 6$ compare to the basic exponential function $f(x) = 2^x$?

Tip: The horizontal asymptote of an exponential function is affected by the constant term $c$.