### Home > CALC > Chapter 1 > Lesson 1.1.1 > Problem1-5

1-5.

Quickly sketch the function $g ( x ) = \sqrt { 16 - x ^ { 2 } }$.

You should recognize this function as a semicircle with radius $4$, centered at the origin.

1. State the domain and range of $g\left(x\right)$.

2. Use geometry to find $A(g, 0 ≤ x ≤ 4)$.
On the graph of $g(x)$, shade the region $A(g,0≤x≤ 4)$. Observe that this area is $\frac{1}{4}$ the area of a complete circle, and $\frac{1}{2}$ the area of the semicircle, $g(x)$.
3. Find $A(g, - 4 ≤ x ≤ 4)$.