Question

a function of the form ( f(x) = ab^x ) is modified so that the ( b ) value remains the same but the ( a ) value is increased by 3. how do the domain and range of the new function compare to the domain and range of the original function?
check all that apply.

• the range stays the same
• the range becomes ( y > 3 )
• the domain stays the same
• the domain becomes ( x > 3 )
• the range becomes ( y > 3 )
• the domain becomes ( x > 3.2 )

Explanation:

For the original function \(f(x)=ab^x\) (assuming this is an exponential function, with \(a>0, b>0, b
eq1\)):

1. Domain: All real numbers, since any real number can be substituted for \(x\) in an exponential function. Increasing the value of \(a\) (while keeping it positive, as it's a standard exponential function) does not restrict or expand the valid inputs for \(x\), so the domain stays the same.
2. Range: For \(a>0\), the original range is all positive real numbers (\(y>0\)). If \(a\) is increased but remains positive, the function still only outputs positive real numbers. The range does not change because it is still all positive \(y\)-values, just the function's outputs are scaled upward, but the set of possible values remains \(y>0\).

Answer:

• The range stays the same
• The domain stays the same