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)=21.4^x the graph dropdown arrow exponentially grows. exponentially decays.

Explanation:

Step1: Identify growth/decay type

For exponential functions $f(x)=a^{kx}$, if $k>0$, it grows. Here $k=1.4>0$, so the graph exponentially grows.

Step2: Calculate f(0)

Substitute $x=0$ into $f(x)$:
$f(0)=2^{1.4\times0}=2^0=1$

Step3: Calculate f(1)

Substitute $x=1$ into $f(x)$:
$f(1)=2^{1.4}\approx2.639$

Answer:

The graph exponentially grows.
Second coordinate for $x=0$: $1$
Second coordinate for $x=1$: $\approx2.639$