Question

answer preview:
the graph of the exponential function ( f ) is shown, where ( y = f(x) ). the ( y )-
intercept of the graph is ( (0, y) ). what is the value of ( y )?

Explanation:

Step1: Recall the definition of y - intercept

The y - intercept of a function \(y = f(x)\) is the value of \(y\) when \(x = 0\).

Step2: Use the given form of the y - intercept

We are given that the y - intercept is \((0,y)\). For the exponential function \(y = f(x)\), when \(x = 0\), we substitute \(x = 0\) into the function.
Let the general form of an exponential function be \(y=a\cdot b^{x}\). When \(x = 0\), \(y=a\cdot b^{0}=a\) (since \(b^{0}=1\) for \(b
eq0\)).
From the graph, when \(x = 0\), we can directly read the value of \(y\).

Answer:

\(-1\)