Question

which graph represents the function $f(x)=2^{x}+2$?

Explanation:

Step1: Find the y - intercept

The y - intercept of a function \(y = f(x)\) is found by setting \(x = 0\). For the function \(f(x)=2^{x}+27\), when \(x = 0\), we use the property \(a^{0}=1\) for \(a
eq0\). So \(f(0)=2^{0}+27\).
Since \(2^{0}=1\), then \(f(0)=1 + 27=28\).

Step2: Analyze the general form of the exponential - function

The function \(y = 2^{x}\) is an exponential growth function with a horizontal asymptote at \(y = 0\). The function \(y=2^{x}+27\) is a vertical shift of the function \(y = 2^{x}\) up by 27 units, and its horizontal asymptote is at \(y = 27\). But we can also just focus on the y - intercept for this multiple - choice problem. Since the y - intercept is \((0,28)\), and none of the given graphs match this (it seems there might be a typo in the function and it was perhaps meant to be \(f(x)=2^{x}+2\) or \(f(x)=2^{x}+3\)). Assuming the function was \(f(x)=2^{x}+2\):
When \(x = 0\), \(f(0)=2^{0}+2=1 + 2=3\).

Answer:

B. \((0,3)\) (assuming the function was meant to be \(f(x)=2^{x}+2\) based on the given options)