Question

What is the equation of g(x)? g(x) = 10x â€"" 3 g(x) = 10x 3 g(x) = 10x â€"" 3 g(x) = 10x 3.

Answer 1

The equation of g(x) is $\rm g(x) = 10^{x-3}$.

Given that,

The graphs of f(x) = 10x and its translation, g(x), are shown.

We have to determine,

What is the equation of g(x)?

According to the question,

The given graphs of two functions f(x) and g(x).

The function f(x) is an exponential function and is given by:

$\rm f(x) = 10^x$

To find the equation for the transformed function g(x).

We could see that the graph of the function g(x) passes through points (3,1), (4,10), (5,100), and so on.

This means that the equation or the expression for the function g(x) is given by:

$\rm g(x) = 10 ^{x-3}$

Substitute the value of x = 3 in the function g(x),

$\rm g(x) = 10 ^{x-3}\\\\g(3) = 10^{3-3}\\\\g(3) = 10^0\\\\g(3) = 1$

Substitute the value of x = 4 in the function g(x),

$\rm g(x) = 10 ^{x-3}\\\\g(4) = 10^{4-3}\\\\g(3) = 10^1\\\\g(3) = 10$

Hence, The equation of g(x) is $\rm g(x) = 10^{x-3}$.

For more details refer to the link given below.

brainly.com/question/13148696