Question

1. f(x)=2^x

parent function:____
domain:____
range:____

Explanation:

Step1: Calculate y - values for given x - values

When \(x=-1\), \(y = 2^{-1}=\frac{1}{2}\); when \(x = 0\), \(y=2^{0}=1\); when \(x = 1\), \(y = 2^{1}=2\); when \(x = 2\), \(y=2^{2}=4\); when \(x = 3\), \(y=2^{3}=8\).

Step2: Determine the domain

The domain of an exponential function \(y = a^{x}\) (\(a>0,a
eq1\)) is all real numbers, so for \(y = 2^{x}\), the domain is \((-\infty,\infty)\).

Step3: Determine the range

Since \(2^{x}>0\) for all real - valued \(x\), the range is \((0,\infty)\).

Step4: Identify the parent function

The parent function of \(y = 2^{x}\) is \(y = a^{x}\) with \(a = 2\), which is an exponential function of the form \(y=a^{x}\) (\(a>0,a
eq1\)).

Answer:

x	y
0	1
1	2
2	4
3	8

Parent Function: \(y = a^{x}(a = 2)\)
Domain: \((-\infty,\infty)\)
Range: \((0,\infty)\)