What is the $$ x $$-intercept of the graph of $$ f(x)=\log _{3}(x+4) $$ ? a.) $$ (-4,0) $$ b.) $$ (-3,0) $$ c.) $$ (1,0) $$ d.) $$ (0,0) $$

Question

UpStudy AI · Accepted Answer

To find the $$ x $$-intercept of the function $$ f(x) = \log_3(x + 4) $$, we need to determine the value of $$ x $$ when $$ f(x) = 0 $$.

1. **Set the function equal to zero:**
   $$
   \log_3(x + 4) = 0
   $$

2. **Convert the logarithmic equation to its exponential form:**
   $$
   3^0 = x + 4
   $$
   $$
   1 = x + 4
   $$

3. **Solve for $$ x $$:**
   $$
   x = 1 - 4
   $$
   $$
   x = -3
   $$

4. **Determine the $$ x $$-intercept:**
   The $$ x $$-intercept is the point where the graph crosses the $$ x $$-axis, which occurs at $$ (x, 0) $$. Substituting $$ x = -3 $$, we get:
   $$
   (-3, 0)
   $$

**Answer:**  
**b.) $$ (-3,0) $$**
The $$ x $$-intercept is $$ (-3, 0) $$.

What is the -intercept of the graph of ?
a.)
b.)
c.)
d.)

Solución de inteligencia artificial de Upstudy

Responder

Solución

Extra Insights

preguntas relacionadas

Latest Pre Algebra Questions

What is the -intercept of the graph of ? a.) b.) c.) d.)