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 2. how do the domain and range of the new function compare to the domain and range of the original function? choose two correct answers.
the range becomes $y > 2$
the range stays the same.
the domain becomes $x \geq 2$
the range becomes $y \geq 2$
the domain stays the same.
the domain becomes $x > 2$.

Explanation:

Step1: Analyze original function domain

For $f(x)=ab^x$ (where $b>0, b
eq1$), $x$ can be any real number.

Step2: Analyze modified function domain

New function is $f(x)=(a+2)b^x$. $x$ still accepts all real numbers, so domain stays same.

Step3: Analyze original function range

Original range: if $a>0$, $y>0$; if $a<0$, $y<0$.

Step4: Analyze modified function range

When $a$ is increased by 2, new leading coefficient is $a+2$. Assuming original $a>0$ (standard exponential growth), new range is $y>2$.

Answer:

• The domain stays the same.
• The range becomes $y > 2$