Starting with the graph of $$ f(x)=8^{x} $$, write the equation of the graph that results from a. reflecting $$ f(x) $$ about the $$ y $$-axis. $$ y= $$ b. shifting $$ f(x) 5 $$ units right. $$ y= $$ c. shifting $$ f(x) 1 $$ units downward.

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To transform the function $$ f(x) = 8^x $$ according to the specified operations, we can apply the following steps:

### a. Reflecting $$ f(x) $$ about the $$ y $$-axis

To reflect a function about the $$ y $$-axis, we replace $$ x $$ with $$ -x $$. Therefore, the equation of the reflected function is:

$$
y = f(-x) = 8^{-x}
$$

### b. Shifting $$ f(x) $$ 5 units right

To shift a function to the right by $$ c $$ units, we replace $$ x $$ with $$ x - c $$. In this case, $$ c = 5 $$. Thus, the equation of the shifted function is:

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

### c. Shifting $$ f(x) $$ 1 unit downward

To shift a function downward by $$ d $$ units, we subtract $$ d $$ from the entire function. Here, $$ d = 1 $$. Therefore, the equation of the shifted function is:

$$
y = f(x) - 1 = 8^x - 1
$$

### Summary of the results:

a. $$ y = 8^{-x} $$

b. $$ y = 8^{x - 5} $$

c. $$ y = 8^x - 1 $$
a. $$ y = 8^{-x} $$ b. $$ y = 8^{x - 5} $$ c. $$ y = 8^x - 1 $$

Starting with the graph of , write the equation of the graph that results from
a. reflecting about the -axis.

b. shifting units right.

c. shifting units downward.

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Starting with the graph of , write the equation of the graph that results from a. reflecting about the -axis. b. shifting units right. c. shifting units downward.