Question

a graph of an exponential function w(x) is shown. use the graph to find the y-intercept and asymptote.

Explanation:

Step1: Find the y - intercept

The y - intercept of a function is the value of the function when \(x = 0\). From the graph, when \(x=0\), we look at the point where the graph intersects the y - axis. The graph intersects the y - axis at \((0,2)\), so the y - intercept is \(2\).

Step2: Find the asymptote

An asymptote is a line that the graph of a function approaches but never touches (or touches at infinity). For the given exponential function, we observe the behavior of the graph as \(x\) increases. The graph approaches the line \(y = 0\) (the x - axis) as \(x\) gets larger. So the horizontal asymptote is \(y=0\).

Answer:

The y - intercept of \(w(x)\) is \(2\) and the horizontal asymptote is \(y = 0\).