Question

select the functio f(x)=\sqrt{x + 4} and check the show values box. use the x - der to aid in completing parts 1 through 3 below. use the interactive igure to find your answer. use the left and right arrow k ys to move along a slider as needed. click here to launch the interactive figure. ... (some content about f(0) is partially shown) \bigcirc b. f(0) has no value part 2: find the value of f(-3). select the correct choice below and, if necessary, fill in the answer box to complete your choice. \bigcirc \checkmark a. f(-3)=1 \bigcirc b. f(-3) has no value part 3: find the value of f(-6). select the correct choice below and, if necessary, fill in the answer box to complete your choice. \bigcirc a. f(-6)=\square \bigcirc b. f(-6) has no value

Explanation:

Step1: Find domain of $f(x)$

For $f(x)=\sqrt{x+4}$, the expression under the square root must be non-negative:
$x+4\geq0 \implies x\geq-4$

Step2: Calculate $f(0)$

Substitute $x=0$ into $f(x)$:
$f(0)=\sqrt{0+4}=\sqrt{4}=2$

Step3: Verify $f(-3)$ (already marked correct)

Substitute $x=-3$ into $f(x)$:
$f(-3)=\sqrt{-3+4}=\sqrt{1}=1$

Step4: Evaluate $f(-6)$

Check if $x=-6$ is in the domain: $-6 < -4$, so the expression under the square root is negative, which is not defined for real numbers.

Answer:

Part 1: A. $f(0)=2$
Part 2: A. $f(-3)=1$
Part 3: B. $f(-6)$ has no value