Question

The graphs of f(x) = 5x and its translation, g(x), are shown on the graph.

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, 5) and (2, 25). g (x) approaches y = negative 10 in quadrant 2 and increases into quadrant 1. It goes through (0, negative 9), (1, negative 5), (2, 15).

What is the equation of g(x)?

g(x) = 5x – 9
g(x) = 5x – 10
g(x) = 5x – 9
g(x) = 5x – 10

Answer 1

According to the function transformations, the equation of function g(x) is $g(x) = 5^x - 10$

How to determine the equation of g(x)?

The complete question is in the attachment

The function f(x) is given as:

$f(x) = 5^x$

From the attached graph, we can see that the function f(x) is 10 units down to get g(x).

This is so because the y values of g(x) are 10 less than the corresponding y values of f(x)

This transformation is represented by:

(x, y) => (x, y - 10)

So, we have:

g(x) = f(x) - 10

Substitute $f(x) = 5^x$

$g(x) = 5^x - 10$

Hence, the equation of function g(x) is $g(x) = 5^x - 10$

Read more about function transformations at:

https://brainly.com/question/3381225

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