Question

Suppose the graph of f(x)=x^2 is translated 3 units eight and 1 unit down. If the resulting graph represents g(x), what is the value of g(2.7)?

Answer 1

The value of g(2.7) is 31.49.

Explanation:

Translations of a function:

Suppose that we have a function f(x).

The translation of f(x) a units to the left is given by g(x) = f(x+a).

The translation of f(x) a units to the right is given by g(x) = f(x-a).

The translation of f(x) a units up is given by g(x) = f(x) + a.

The translation of f(x) a units down is given by g(x) = f(x) - a.

Suppose the graph of f(x)=x^2 is translated 3 units right and 1 unit down.

Three units right:

`g(x) = f(x+3) = (x+3)^2`

One unit down:

`g(x) = f(x+3) - 1 = (x+3)^2 - 1`

What is the value of g(2.7)?

This is g when
`x = 2.7`. So

`g(2.7) = (2.7+3)^2 - 1 = (5.7)^2 - 1 = 31.49`

The value of g(2.7) is 31.49.