Graph, Then state the y-intercept, Common Ratio, Growth/Decay Doma y=2(4)^x Answer Attemptiout of 99 y - intercept: square Common Ratio: 4 Growth or Decay: square Domain: square v Range: square Asymptote: square

To graph the function $y=2(4)^{x}$, we can start by plotting a few points and then connect them to form a curve.<br /><br />Let's choose some values for $x$ and calculate the corresponding $y$ values:<br /><br />When $x=0$, $y=2(4)^{0}=2(1)=2$<br />When $x=1$, $y=2(4)^{1}=2(4)=8$<br />When $x=-1$, $y=2(4)^{-1}=2(\frac{1}{4})=\frac{1}{2}$<br /><br />Now, let's plot these points on a coordinate plane and connect them to form a curve.<br /><br />The y-intercept is the point where the curve intersects the y-axis. In this case, the y-intercept is $(0,2)$.<br /><br />The common ratio is the factor by which each term is multiplied to get the next term. In this case, the common ratio is 4.<br /><br />Since the base of the exponent (4) is greater than 1, the function represents exponential growth.<br /><br />The domain of the function is the set of all possible values of $x$. In this case, the domain is all real numbers, or $(-\infty, \infty)$.<br /><br />The range of the function is the set of all possible values of $y$. In this case, the range is $(0, \infty)$.<br /><br />The asymptote is a line that the curve approaches but never touches. In this case, the horizontal asymptote is the x-axis, or $y=0$.<br /><br />So, the final answers are:<br /><br />y-intercept: $(0,2)$<br />Common Ratio: 4<br />Growth or Decay: Growth<br />Domain: $(-\infty, \infty)$<br />Range: $(0, \infty)$<br />Asymptote: $y=0$