Answer:
The third option is correct
[tex]\displaystyle h(x)=\left ( \frac{10}{3} \right )^x[/tex]
[tex]\displaystyle g(x)=\left ( \frac{7}{4} \right )^x[/tex]
[tex]\displaystyle f(x)=\left ( \frac{9}{8} \right )^x[/tex]
Step-by-step explanation:
Exponential function
The exponential function is usually expressed as
[tex]f(x)=Cr^{kx}[/tex]
If both C and k are positive, then f is increasing in all of its domain. Same happens if both are negative. They all have one point in common: (0,C)
The graph shows three functions, all increasing and in all of them (given the options for the answer) have C=1 and k=1, so the equation for each one is
[tex]f(x)=r^{x}[/tex]
When x=1, f(1)=r lets us know the value of r
From the graph we can see that the value of r is the greatest for h(x). The next value of r is that one for g(x). Finally, f(x) has the smallest r. That means that
[tex]h(1)>g(1)>f(1)[/tex]
We only need to check the options to order h,g,f from greatest to lowest. Since (10/3)=3.3, (9/8)=1.12, (7/4)=1.75 then
h(x) must have [tex]r=\frac{10}{3}[/tex]
g(x) must have [tex]r=\frac{7}{4}[/tex]
f(x) must have [tex]r=\frac{9}{8}[/tex]
So the third option is correct
[tex]\displaystyle h(x)=\left ( \frac{10}{3} \right )^x[/tex]
[tex]\displaystyle g(x)=\left ( \frac{7}{4} \right )^x[/tex]
[tex]\displaystyle f(x)=\left ( \frac{9}{8} \right )^x[/tex]
