Question

what is the range of this exponential function? drag & drop the answer note: use ctrl+d to drag the option via keyboard {y|y < 9} {y|y ≤ 9} {y|y > 9} {y|y ≥ 9} range =

Explanation:

Step1: Recall the range of exponential functions

The general form of an exponential function is \(y = a\cdot b^{x}+k\). For \(b> 1\), as \(x\to-\infty\), \(y\to k\) (horizontal asymptote), and as \(x\to+\infty\), \(y\to+\infty\).

Step2: Analyze the given graph

From the graph, we can observe that the horizontal asymptote is \(y = 9\). Since the exponential function is of the form \(y=a\cdot b^{x}+9\) (\(a>0,b > 1\)), as \(x\to-\infty\), \(y\to9\) (approaching from below), and as \(x\to+\infty\), \(y\to+\infty\). So the range of the function is \(y>9\).

Answer:

\(\{y|y > 9\}\)