Question

q2 week 8
1.
identify each.
function family:
domain:
range:
asymptote:

Explanation:

Step1: Identify Function Family

The graph has a curve that decreases rapidly and then approaches a horizontal line, which is characteristic of an exponential function (specifically, an exponential decay function, part of the exponential function family).

Step2: Determine Domain

The domain of a function is the set of all possible x - values. Looking at the graph, the curve exists for all x - values greater than - 2 (since the graph starts at x=-2 and extends to the right). So the domain is \(x > - 2\) (in interval notation, \((-2,\infty)\)).

Step3: Determine Range

The range of a function is the set of all possible y - values. The graph approaches \(y = 2\) as \(x\) increases, and the y - values are all greater than 2 (since the graph is above \(y = 2\)). So the range is \(y>2\) (in interval notation, \((2,\infty)\)).

Step4: Identify Asymptote

An asymptote is a line that the graph approaches but never touches. The graph approaches the horizontal line \(y = 2\), so the horizontal asymptote is \(y = 2\).

Answer:

• Function Family: Exponential (Decay) Function Family
• Domain: \(x>-2\) (or \((-2,\infty)\))
• Range: \(y > 2\) (or \((2,\infty)\))
• Asymptote: \(y = 2\)