Suppose that the $$ x $$-intercepts of the graph of $$ y=f(x) $$ are -6 and -3 (a) What are the $$ x $$-intercepts of the graph of $$ y=f(x+8) $$ ? The $$ x $$-intercepts of the graph of $$ y=f(x+8) $$ are $$ -14,-11 $$. (Use a comma lo separate answers as needed.) (b) What are the $$ x $$-intercepts of the graph of $$ y=1(x-7) $$ ? The $$ x $$-intercepts of the graph of $$ ~ $$ $$ =f(x-7) $$ are 1,4 (Use a comma to separale answers as needed.) (c) What ore the $$ x $$-intercepts of the graph of $$ y=31(x) $$ ? The $$ x $$-iniercepts of the graph of $$ y=3 t(x) $$ are $$ -6,-3 $$. (Use a comma to separale answers as needed.) (d) What are tho $$ x $$-intercepts of the graph of $$ y=f(-x) $$ ? The $$ x $$-intercepts of the graph of $$ y=f(-x) $$ are $$ \square $$. (Use a comma to sdarate answers as needed.)

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Let's analyze each part of the problem step by step.

### Given Information
The $$ x $$-intercepts of the graph of $$ y = f(x) $$ are at $$ x = -6 $$ and $$ x = -3 $$. This means that $$ f(-6) = 0 $$ and $$ f(-3) = 0 $$.

### (a) $$ x $$-intercepts of $$ y = f(x + 8) $$
To find the $$ x $$-intercepts of $$ y = f(x + 8) $$, we set $$ f(x + 8) = 0 $$. This occurs when:
$$
x + 8 = -6 \quad \text{or} \quad x + 8 = -3
$$
Solving these equations:
1. $$ x + 8 = -6 $$ leads to $$ x = -14 $$
2. $$ x + 8 = -3 $$ leads to $$ x = -11 $$

Thus, the $$ x $$-intercepts of the graph of $$ y = f(x + 8) $$ are $$ -14, -11 $$.

### (b) $$ x $$-intercepts of $$ y = f(x - 7) $$
To find the $$ x $$-intercepts of $$ y = f(x - 7) $$, we set $$ f(x - 7) = 0 $$. This occurs when:
$$
x - 7 = -6 \quad \text{or} \quad x - 7 = -3
$$
Solving these equations:
1. $$ x - 7 = -6 $$ leads to $$ x = 1 $$
2. $$ x - 7 = -3 $$ leads to $$ x = 4 $$

Thus, the $$ x $$-intercepts of the graph of $$ y = f(x - 7) $$ are $$ 1, 4 $$.

### (c) $$ x $$-intercepts of $$ y = 3f(x) $$
The $$ x $$-intercepts of $$ y = 3f(x) $$ are the same as those of $$ y = f(x) $$ because multiplying by a non-zero constant does not change the $$ x $$-intercepts. Therefore, the $$ x $$-intercepts of the graph of $$ y = 3f(x) $$ are $$ -6, -3 $$.

### (d) $$ x $$-intercepts of $$ y = f(-x) $$
To find the $$ x $$-intercepts of $$ y = f(-x) $$, we set $$ f(-x) = 0 $$. This occurs when:
$$
-x = -6 \quad \text{or} \quad -x = -3
$$
Solving these equations:
1. $$ -x = -6 $$ leads to $$ x = 6 $$
2. $$ -x = -3 $$ leads to $$ x = 3 $$

Thus, the $$ x $$-intercepts of the graph of $$ y = f(-x) $$ are $$ 6, 3 $$.

### Final Answers
(a) $$ -14, -11 $$  
(b) $$ 1, 4 $$  
(c) $$ -6, -3 $$  
(d) $$ 6, 3 $$
(a) $$ -14, -11 $$ (b) $$ 1, 4 $$ (c) $$ -6, -3 $$ (d) $$ 6, 3 $$

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