Question

without graphing, describe the shape of the graph of the function. find the second coordinates of the points with first coordinates 0 and 1.\\(f(x)=2^{1.4x}\\)\\(\dots\\)\\(\text{the graph exponentially grows.}\\)\\(\text{find the second coordinates of the given first coordinates.}\\)\\(\

$$\begin{array}{c|c|c}x&0&1\\\\f(x)=2^{1.4x}&f(0)=\\square&f(1)=\\square\\end{array}$$

\\)\\((\text{round to one decimal place as needed})\\)

Explanation:

Step1: Substitute x=0 into function

$f(0)=2^{1.4\times0}=2^0$

Step2: Evaluate the exponential term

$2^0=1$

Step3: Substitute x=1 into function

$f(1)=2^{1.4\times1}=2^{1.4}$

Step4: Calculate and round the value

$2^{1.4}\approx2.6$

Answer:

$f(0)=1$, $f(1)=2.6$
The graph is an exponential growth curve that passes through the points $(0,1)$ and $(1,2.6)$, increasing rapidly as $x$ increases, approaching $0$ as $x$ approaches negative infinity.