Angles in Circles
Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.
Arcs in Circles
A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.

![### Mathematical Function Transformation
#### Function Representation
The function presented is:
\[ r(x) = -\frac{x^2}{3} + 2 \]
#### Task
Determine the more basic function that has been shifted, reflected, stretched, or compressed.
#### Analysis
This function can be broken down into transformations of the basic quadratic function \( f(x) = x^2 \):
1. **Reflection**: The coefficient \(-\frac{1}{3}\) represents a reflection over the x-axis.
2. **Compression**: The factor \(\frac{1}{3}\) indicates that the function is vertically compressed by a factor of 3.
3. **Vertical Shift**: The "+2" at the end of the function indicates that the graph is shifted upward by 2 units.
Thus, the transformations applied to the basic function \( f(x) = x^2 \) to obtain \( r(x) \) include a reflection over the x-axis, a vertical compression by a factor of \(\frac{1}{3}\), and an upward shift by 2 units.
Understanding these transformations is crucial for analyzing the behavior and shape of the given function's graph.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F455c53c9-baa8-43c7-99b3-798863e46488%2Fc2cb920d-ceb8-4ed7-a199-b41374e6ca2d%2F724qhk_processed.jpeg&w=3840&q=75)

Step by step
Solved in 2 steps with 2 images









