Question

For the graph, which are possible functions ƒ, g, and h?

Answer 1

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Explanation:

Answer 2

The third option is correct

`\displaystyle h(x)=\left ( (10)/(3) \right )^x`

`\displaystyle g(x)=\left ( (7)/(4) \right )^x`

`\displaystyle f(x)=\left ( (9)/(8) \right )^x`

Explanation:

Exponential function

The exponential function is usually expressed as

`f(x)=Cr^(kx)`

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

`f(x)=r^(x)`

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

`h(1)>g(1)>f(1)`

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
`r=(10)/(3)`

g(x) must have
`r=(7)/(4)`

f(x) must have
`r=(9)/(8)`

So the third option is correct

`\displaystyle h(x)=\left ( (10)/(3) \right )^x`

`\displaystyle g(x)=\left ( (7)/(4) \right )^x`

`\displaystyle f(x)=\left ( (9)/(8) \right )^x`