Answer:
y = [tex]3 (\frac{1}{3} )^{x}[/tex]
Step-by-step explanation:
Step 1:
Check the y-intercept; in the graph, when x = 0, y = 3. Which equation satisfies this?
y = [tex]\frac{1}{3}[/tex] [tex](3)^{x}[/tex] = [tex]\frac{1}{3}[/tex] [tex](3)^{0}[/tex] = [tex]\frac{1}{3}[/tex] ❌
y = [tex]3 (\frac{1}{3} )^{x}[/tex] = [tex]3 (\frac{1}{3} )^{0}[/tex] = 3 ✅
y = [tex](\frac{1}{2} )^{x}[/tex] + 2 = [tex](\frac{1}{2} )^{0}[/tex] + 2 = 3 ✅
So the last two equations are possible.
Step 2:
Now check the y-value on the graph for any other x-value, whose corresponding y-value can be easily estimated from the graph.
For example, when x = 2, the y-value is between 0 and 1.
• 2nd equation: y = [tex]3 (\frac{1}{3} )^{x}[/tex] = [tex]3 (\frac{1}{3} )^{2}[/tex] = 0.333 ✅
• 3rd equation: y = [tex](\frac{1}{2} )^{x}[/tex] + 2 = y = [tex](\frac{1}{2} )^{2}[/tex] + 2 = 2. 25 ❌
∴ 2nd equation (y = [tex]3 (\frac{1}{3} )^{x}[/tex] ) is the one being represented by the graph.
