Answer:
[tex]g(2) = 9[/tex]
[tex]x = 1[/tex]
[tex]g(0) = 1[/tex]
[tex]g(x)=3^x[/tex]
Step-by-step explanation:
To find g(2), find the y-value when x = 2.
From inspection of the graph, g(2) = 9.
To find x when g(x) = 3, find the x-value when y = 3.
From inspection of the graph, g(1) = 3, so x = 1.
To find g(0), find the y-value when x = 0.
From inspection of the graph, g(0) = 1.
Therefore, we have determined the following ordered pairs:
The given graph is a graph of an exponential function.
General form of an exponential function:
[tex]f(x)=ab^x[/tex]
where:
- a is the initial value (y-intercept).
- b is the base (growth/decay factor) in decimal form.
The y-intercept is when x = 0.
As the y-intercept is 1, a = 1:
[tex]\implies g(x)=(1)b^x[/tex]
[tex]\implies g(x)=b^x[/tex]
To find the value of b, substitute one of the ordered pairs into the function and solve for b:
[tex]\begin{aligned}g(x)=b^x&\phantom{=}\\\implies g(2)=b^2&=9\\ \sqrt{b^2}&=\sqrt{9}\\b&=3\end{aligned}[/tex]
Therefore, the rule for the graphed function is:
[tex]\boxed{g(x)=3^x}[/tex]
