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 to separate answers as needed.) (b) What are the $$ x $$-intercepts of the graph of $$ y=f(x-7) $$ ? The $$ x $$-intercepts of the graph of $$ y=f(x-7) $$ are (Use a comma to separale answers as needed.)

Question

UpStudy AI · Accepted Answer

To find the $$ x $$-intercepts of the transformed functions $$ y = f(x + 8) $$ and $$ y = f(x - 7) $$, we need to understand how the transformations affect the $$ x $$-intercepts.

### (a) Finding the $$ x $$-intercepts of $$ y = f(x + 8) $$

The $$ x $$-intercepts of the function $$ y = f(x) $$ are the values of $$ x $$ for which $$ f(x) = 0 $$. Given that the $$ x $$-intercepts of $$ y = f(x) $$ are -6 and -3, we can find the $$ x $$-intercepts of $$ y = f(x + 8) $$ by setting $$ x + 8 = 0 $$ for each intercept.

1. For the intercept $$ x = -6 $$:
   $$
   -6 + 8 = 2 \quad \Rightarrow \quad x = -6 \text{ becomes } x = -6 - 8 = -14
   $$

2. For the intercept $$ x = -3 $$:
   $$
   -3 + 8 = 5 \quad \Rightarrow \quad x = -3 \text{ becomes } x = -3 - 8 = -11
   $$

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

### (b) Finding the $$ x $$-intercepts of $$ y = f(x - 7) $$

Similarly, we can find the $$ x $$-intercepts of $$ y = f(x - 7) $$ by setting $$ x - 7 = 0 $$ for each intercept.

1. For the intercept $$ x = -6 $$:
   $$
   -6 - 7 = -13 \quad \Rightarrow \quad x = -6 \text{ becomes } x = -6 + 7 = 1
   $$

2. For the intercept $$ x = -3 $$:
   $$
   -3 - 7 = -10 \quad \Rightarrow \quad x = -3 \text{ becomes } x = -3 + 7 = 4
   $$

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

### Final Answers:
(a) The $$ x $$-intercepts of the graph of $$ y = f(x + 8) $$ are $$ -14, -11 $$.

(b) The $$ x $$-intercepts of the graph of $$ y = f(x - 7) $$ are $$ 1, 4 $$.
(a) The $$ x $$-intercepts of $$ y = f(x + 8) $$ are $$ -14, -11 $$. (b) The $$ x $$-intercepts of $$ y = f(x - 7) $$ are $$ 1, 4 $$.

Solución de inteligencia artificial de Upstudy

Responder

Solución

The Deep Dive

preguntas relacionadas

Latest Algebra Questions