Question

A function of the form f(x) = abx 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? Check all that apply. The range stays the same. The range becomes y > 2. The domain stays the same. The domain becomes x > 2. The range becomes y ≥ 2. The domain becomes x ≥ 2.

Answer 1

We are given

$f(x)=a(b)^x$

Here , we are given that it is modified so that the 'b' value remains the same but the 'a' value is increased by 2

so, we can write our function as

$f(x)=(a+2)(b)^x$

Domain:

Domain is all possible values of x for which any function is defined

We can see that there is no change in x

so, domain will remain same

Range:

Range is all possible value of y for which x is defined

so, lowest value of y will be 2

so, range is

$(-\infty,\infty)$

Answer is

domain will remain same

range is $(-\infty,\infty)$

Answer 2

Answer:

The domain and range of the function will be same after the modification.

Step-by-step explanation:

$\text{The function is given to be : }f(x) = a\cdot b^x$

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

$\text{The modified function will be : }f(x) = (a+2)\cdot b^x$

⇒ 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.