Question

the function $f$ is defined by $f(x)=2^{x}$.which of the following statements is true about the values of $f$?select all that apply.when the input $x$ increases by 1, the value of $f$ increases by 2.when the input $x$ increases by 1, the value of $f$ increases by a factor of 2.when the input $x$ increases by 3, the value of $f$ increases by 8.when the input $x$ increases by 3, the value of $f$ increases by a factor of 8.when the input $x$ increases by 4, the value of $f$ increases by a factor of 4.

Explanation:

Step1: Test x increase by 1

Let input be $x$, new input $x+1$.
$f(x+1)=2^{x+1}=2\times2^x=2f(x)$

Step2: Test x increase by 3

Let input be $x$, new input $x+3$.
$f(x+3)=2^{x+3}=8\times2^x=8f(x)$

Step3: Test x increase by 4

Let input be $x$, new input $x+4$.
$f(x+4)=2^{x+4}=16\times2^x=16f(x)$

Answer:

When the input $x$ increases by 1, the value of $f$ increases by a factor of 2.
When the input $x$ increases by 3, the value of $f$ increases by a factor of 8.