Answer:
The domain and range of the function will be same after the modification.
Step-by-step explanation:
[tex]\text{The function is given to be : }f(x) = a\cdot b^x[/tex]
Domain and Range of the function f(x) is the set of real numbers
Now, the value of the given function f(x) is modified such that the value of b remains same but the value of a is increased by 2
[tex]\text{The modified function will be : }f(x) = (a+2)\cdot b^x[/tex]
⇒ The domain and range of the modified function is also the set of all real numbers.
Therefore, The domain and range of the function will be same after the modification.
The domain and the range of a function are the set of input and output values, the function can take.
The correct statements are: (a) The range stays the same. and (c) The domain stays the same.
The parent function is given as:
[tex]\mathbf{f(x) = ab^x}[/tex]
There is no restriction on the x and y values of the above function. So, the domain and the range are:
[tex]\mathbf{Domain = Range = (-\infty,\infty)}[/tex]
When the function is updated, we have:
[tex]\mathbf{g(x) = 2f(x)}[/tex]
[tex]\mathbf{g(x) = 2ab^x}[/tex]
Similarly, there is no restriction on the x and y values of [tex]\mathbf{g(x) = 2ab^x}[/tex]
So, the domain and the range of the new function are: [tex]\mathbf{Domain = Range = (-\infty,\infty)}[/tex]
Hence, the correct statements are: (a) The range stays the same. and (c) The domain stays the same.
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