Question

The graphs of f(x) = 10x and its translation, g(x), are shown. On a coordinate plane, 2 exponential functions are shown. f (x) approaches y = 0 in quadrant 2 and increases into quadrant 1. It crosses the y-axis at (0, 1) and goes through (1, 10) and (2, 100). g (x) approaches y = 0 in quadrant 2 and increases into quadrant 2. It goes through (3, 1), (4, 10), and (5, 100). What is the equation of g(x)? g(x) = 10x – 3 g(x) = 10x + 3 g(x) = 10x – 3 g(x) = 10x + 3

Answer 1

The answer is option A if you don't wanna read all of that ^

Answer 2

`g(x)=(10)^(x-3)`

Explanation:

* Lets explain how to solve the problem

- The form of the exponential function is
`f(x)=a(b)^(x)` , where

a is the initial amount (x = 0) , b is the growth factor

- If b > 1 , then the function is exponential growth function

- If 0 < b < 1 , then the function is exponential decay function

- If the function translated horizontally by h units to the right , then

the new function is
`g(x)=a(b)^(x-h)`

- If the function translated horizontally by h units to the left , then

the new function is
`g(x)=a(b)^(x+h)`

- If the function translated vertically by k units up , then the new

function is
`g(x)=a(b)^(x)+k`

- If the function translated vertically by k units down , then the new

function is
`g(x)=a(b)^(x)-k`

* Lets solve the problem

∵ f(x) is an exponential function

∵ Points (0 , 1) , (1 , 10) , (2 , 100) belong to f(x)

- g(x) is the image of f(x) after translation

∵ Points (3 , 1) , (4 , 10) , (5 , 100) belong to g(x)

∵ point (0 , 1) on f(x) becomes (3 , 1) on g(x)

∵ point (1 , 10) on f(x) becomes (4 , 10) on g(x)

∵ point (2 , 100) on f(x) becomes (5 , 100) in g(x)

∵ All the y-coordinates of the points on the function f(x) are the same

with the y-coordinates of the points on the function g(x)

∴ There is no vertical translation

∵ The x-coordinates of the points on the function f(x) are added by

3 units to give the x-coordinates of the points on the function g(x)

∴ f(x) is translated 3 units to the right

∵
`f(x)=(10)^(x)`

∴
`g(x)=(10)^(x-3)`

- Look to the attached graph for more understand

# Red graph represents f(x)

# Blue graph represents g(x)