Find the domain and intercepts. $$ f(x)=\sqrt{x+36} $$ Find the domain Select the correct choi A. The domain of the function $$ f(x) $$ is Bype your answer in interval no B. The domain is all real numbers.

Question

UpStudy AI · Accepted Answer

To find the domain of the function $$ f(x) = \sqrt{x + 36} $$, we need to determine the values of $$ x $$ for which the expression under the square root is non-negative, since the square root of a negative number is not defined in the real number system.

### Step 1: Set the expression under the square root greater than or equal to zero.

$$
x + 36 \geq 0
$$

### Step 2: Solve the inequality.

Subtract 36 from both sides:

$$
x \geq -36
$$

### Step 3: Write the domain in interval notation.

The domain of $$ f(x) $$ is all values of $$ x $$ that are greater than or equal to -36. In interval notation, this is expressed as:

$$
[-36, \infty)
$$

### Step 4: Find the intercepts.

#### x-intercept:
To find the x-intercept, set $$ f(x) = 0 $$:

$$
\sqrt{x + 36} = 0
$$

Squaring both sides gives:

$$
x + 36 = 0
$$

Solving for $$ x $$:

$$
x = -36
$$

So, the x-intercept is at the point $$(-36, 0)$$.

#### y-intercept:
To find the y-intercept, evaluate $$ f(0) $$:

$$
f(0) = \sqrt{0 + 36} = \sqrt{36} = 6
$$

So, the y-intercept is at the point $$(0, 6)$$.

### Summary:
- The domain of the function $$ f(x) $$ is $$[-36, \infty)$$.
- The x-intercept is at $$(-36, 0)$$.
- The y-intercept is at $$(0, 6)$$.

### Final Answer:
A. The domain of the function $$ f(x) $$ is $$[-36, \infty)$$.
The domain of $$ f(x) = \sqrt{x + 36} $$ is all real numbers $$ x $$ such that $$ x \geq -36 $$. In interval notation, this is $$[-36, \infty)$$. The function has an x-intercept at $$(-36, 0)$$ and a y-intercept at $$(0, 6)$$.

Find the domain and intercepts.

Find the domain Select the correct choi
A. The domain of the function is
Bype your answer in interval no
B. The domain is all real numbers.

Upstudy AI Solution

Answer

Solution

Step 1: Set the expression under the square root greater than or equal to zero.

Step 2: Solve the inequality.

Step 3: Write the domain in interval notation.

Step 4: Find the intercepts.

x-intercept:

y-intercept:

Summary:

Final Answer:

Beyond the Answer

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Find the domain and intercepts. Find the domain Select the correct choi A. The domain of the function is Bype your answer in interval no B. The domain is all real numbers.