Question

4.

The graph of an exponential function is given. Which of the following is the correct equation of the function?
5.
Compute the exact value of the function for the given x-value without using a calculator. Show your work for full credit. (2 points)
f(x) = 7x for x = 2

Answer 1

B

Explanation:

EDGE 2020

Answer 2

For the first point, remember this simple rule: every exponential function
`a^x` always returns
`a` when evaluated at
`x = 1`. In fact,
`a^1=a` for every possible base
`a`.

So, we can see that the graph of the exponential passes through the point
`(1,y)` where
`y` appears to be between 1 and 2. So, the only feasible option would be
`y = 1.8^x`, because it passes throught the point
`(1,1.8)` because
`f(1) = 1.8^1 = 1.8`.

The other functions are wrong because:

• 
  `0.45^x` would pass through
  `(1,0.45)`, which would be between 0 and 1 on the y axis
• 
  `2.4^x` would pass through
  `(1,2.4)`, which would be between 2 and 3 on the y axis
• 
  `0.31^x` would pass through
  `(1,0.31)`, which would be between 0 and 1 on the y axis

As for the second question, you simply have to plug in the values: the function

`f(x) = 7^x`

means that you have to choose an input, x, and use it as exponent for 7. So, if you choose x=2, it means that you have to give exponent 2 to 7, i.e. you replace the x with the specific value, 2.

So, the expression becomes

`f(2) = 7^2 = 49`