Question

Use what you know about translations of functions to analyze the graph of the function

f(x) = (0.5) 5 + 8. You may wish to graph it and its parent function, y = 0.5°, on the same axes.
The parent function y = 0.5° is
v across its domain because its base, b, is such that
DONEI
The function, f, shifts the parent function 8 units _____
The function, f, shifts the parent function 5 units _____

Answer 1

The function f(x) shifts the parent function 8 units upward, but does not shift it horizontally.

Answer 2

Step-by-step explanation:The parent function y = 0.5^x is decreasing across its domain because its base, b, is such that 0 < b < 1.

To graph the function f(x) = (0.5)^5 + 8, we can start by graphing the parent function y = (0.5)^x. We can plot a few points for the parent function:

| x | y |

|---|---|

| -2 | 4 |

| -1 | 2 |

| 0 | 1 |

| 1 | 0.5 |

| 2 | 0.25 |

Using these points, we can plot the parent function y = (0.5)^x, which looks like this:

Now, to graph the function f(x) = (0.5)^5 + 8, we can apply the translations to the parent function. The function adds 8 to the output of the parent function, so we can shift the parent function up 8 units to get the graph of f(x). The graph of f(x) is shown below in red, with the parent function in blue for comparison:

As we can see, the function f(x) shifts the parent function up 8 units. It does not shift the parent function horizontally by 5 units, as there is no horizontal translation in the function.