Question

use what you know about translations of functions to analyze the graph of the function f(x) = (0.5)^x-5+8 you may wish to grab it and its parent function y=0.5^x on the same axes
The parent function y=0.5^x is _____ across its domain because its base b is such that

Answer 1

First box is: decreasing

Second box: 0< b< 1

Third box: Up

Fourth box: Right

Answer 2

The parent function y=0.5^x is decreasing across its domain because its base b is such that (0<b<1) and function shifts it 8 units up and 5 units right.

What is translation of a function?

Translation of a function is shifting the function from its original place in the graph.

Types of translation -

• Horizontal shift- Let the parent function is f(x). Thus by replacing parent function with f(x-b) shifts the graph b units right and by replacing parent function with f(x+b) shifts the graph b units left.
• Vertical shift- Let the parent function is f(x). Thus by replacing parent function with f(x)+c shifts the graph c units down and by replacing parent function with f(x)-c shifts the graph b units up.

The functions of the graph given in the problem as,

$f(x) = (0.5)^{x-5}+8$

The parent function of the graph is,

$y=0.5^x$

In the parent function, the 5 units subtracted, and 8 units added outside the function. Thus, the function shifts the parent function 8 units up and 5 units right.

Thus, the parent function y=0.5^x is decreasing across its domain because its base b is such that (0<b<1) and function shifts it 8 units up and 5 units right.

Learn more about the transition of a function here;

https://brainly.com/question/626170