Questions: Give the equation of the exponential function whose graph is shown. y= (Type an exact answer.)

Solution Steps

The general form of an exponential function is \( y = ab^x \), where \( a \) is the initial value (y-intercept) and \( b \) is the base of the exponential function.

From the graph, we can see that when \( x = 0 \), \( y = -1 \). Therefore, the initial value \( a \) is -1.

We can use the point (1, -6) to find the base \( b \). Substitute \( x = 1 \) and \( y = -6 \) into the equation \( y = ab^x \):

\[ -6 = -1 \cdot b^1 \]

Solving for \( b \):

\[ b = 6 \]

Final Answer