graph: $f(x)=2(2)^{x}$ which statements are true about the graph? check all that apply. the y - intercept is…

graph: $f(x)=2(2)^{x}$ which statements are true about the graph? check all that apply. the y - intercept is $(0,2)$. the x - intercept is $(4,0)$. $f(1)=2$ $f(2)=8$ it is a shrink of an exponential growth function. the correct line is shown.

graph: $f(x)=2(2)^{x}$ which statements are true about the graph? check all that apply. the y - intercept is $(0,2)$. the x - intercept is $(4,0)$. $f(1)=2$ $f(2)=8$ it is a shrink of an exponential growth function. the correct line is shown.

Answer

Explanation:

Step1: Find y - intercept

Set $x = 0$ in $f(x)=2(2)^{x}$. Then $f(0)=2(2)^{0}=2\times1 = 2$. So the y - intercept is $(0,2)$.

Step2: Find x - intercept

Set $y = f(x)=0$, so $2(2)^{x}=0$. Since $2^{x}>0$ for all real $x$, there is no x - intercept.

Step3: Calculate $f(1)$

Substitute $x = 1$ into $f(x)=2(2)^{x}$, we get $f(1)=2(2)^{1}=2\times2 = 4$.

Step4: Calculate $f(2)$

Substitute $x = 2$ into $f(x)=2(2)^{x}$, we have $f(2)=2(2)^{2}=2\times4 = 8$.

Step5: Analyze the function form

The function $f(x)=2(2)^{x}=2^{x + 1}$ is an exponential growth function and not a shrink of an exponential growth function.

Answer:

The y - intercept is $(0,2)$. $f(2)=8$