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)?

Answer 1

Answer:

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Step-by-step explanation:

Answer 2

The equation of g(x) is $g(x)=5^x-10$

What is equation?

"It is a mathematical statement which consists of equal symbol between two algebraic expressions."

What is function?

• "It defines the relation between input and output values."
• "In function , for any input value there is exactly one output."

What is translation?

"It is a geometric transformation in which there is change in the position of the geometric structure without change in the shape and size."

For given question,

We have been given two function f(x) and g(x)

where, $f(x)=5^x$

and g(x) is is the translated function of g(x)

We need to find the equation of g(x).

The graph of f(x) is,

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).

The graph of g(x) is,

g (x) approaches y = -10 in quadrant 3 and increases into quadrant 1.

It goes through (0, -9), (1, -5), (2, 15).

Consider the following figure.

The graph of g(x) approaches y = -10 and the graph of f(x) approaches y = 0

This means, the function f(x) is translated 10 units downward.

⇒$f(x)\rightarrow f(x)-10$

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

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