GIVEN:
We are given the following function;
[tex]f(x)=4(0.5)[/tex]
Required;
To graph the function and then find the y-intercept.
Step-by-step solution;
The function given is in the form;
[tex]f(x)=ab^x[/tex]
This is an exponential function and x can take any value, which will determine the value of y. From the function we can determine that the initial value a is the point where x = 0 and at that point we have the y intercept, that is, when x = 0, then y = a.
[tex]\begin{gathered} y=ab^x \\ \\ When\text{ }x=0. \\ \\ y=ab^0 \\ \\ y=a(1) \\ \\ y=a \end{gathered}[/tex]
Therefore, for the function given;
[tex]\begin{gathered} f(x)=4(0.5)^x \\ \\ When\text{ }x=0, \\ \\ f(x)=4(0.5)^0 \\ \\ f(x)=4(1) \\ \\ f(x)=4 \end{gathered}[/tex]
Therefore, the y-intercept here is 4. Note also that the value of b is 0.5, which is less than 1. This indicates that its an exponential decrease (exponential decay). Therefore, its downward sloping from left to right
The graph is shown below;
Therefore,
ANSWER:
Option C is the correct answer.
[tex]y-intercept:(0,4)[/tex]
