Question

in general, the y-intercept of the function $f(x) = a \cdot b^x$ is the point
a. $(0, x)$
b. $(0, a)$
c. $(0, b)$
d. $(0, 1)$

Explanation:

Step1: Recall y-intercept definition

The y - intercept of a function \( F(x) \) is the point where \( x = 0 \), so we substitute \( x = 0 \) into the function \( F(x)=a\cdot b^{x} \).

Step2: Substitute \( x = 0 \) into the function

When \( x = 0 \), we have \( F(0)=a\cdot b^{0} \). Since any non - zero number raised to the power of 0 is 1 (\( b^{0}=1 \) for \( b
eq0 \)), then \( F(0)=a\times1 = a \). So the y - intercept is the point \( (0,a) \).

Answer:

B. \((0, a)\)