(4, 4) 10 12 (-4, –4) (8, –4) (12, –4) Graph of f 3. The figure above shows the graph of the piecewise-linear function f. For –45x< 12, the function g is defined by g(x) = [, 1(1) dr. (a) Does g have a relative minimum, a relative maximum, or neither at x = 10 ? Justify your answer. (b) Does the graph of g have a point of inflection at x = 4 ? Justify your answer. (c) Find the absolute minimum value and the absolute maximum value of g on the interval -4 < x< 12. Justify your answers.
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.
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![### Graph of the Piecewise-Linear Function \( f \)
The graph provided represents a piecewise-linear function \( f \) with specific points marked on the Cartesian plane:
- The graph passes through the points \((-4, -4)\), \((0, 4)\), \((4, 4)\), \((8, -4)\), and \((12, -4)\).
- The function \( f \) forms linear segments between these points, creating a series of peaks and troughs.
### Questions
#### 3. The figure above shows the graph of the piecewise-linear function \( f \). For \( -4 \leq x \leq 12 \), the function \( g \) is defined by
\[
g(x) = \int_{2}^{x} f(t) \, dt.
\]
#### (a) Does \( g \) have a relative minimum, a relative maximum, or neither at \( x = 10 \)? Justify your answer.
#### (b) Does the graph of \( g \) have a point of inflection at \( x = 4 \)? Justify your answer.
#### (c) Find the absolute minimum value and the absolute maximum value of \( g \) on the interval \(-4 \leq x \leq 12\). Justify your answers.
#### (d) For \( -4 \leq x \leq 12 \), find all intervals for which \( g(x) \leq 0 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5ea9b136-d67a-4b38-a71c-ee23174a22b9%2F15d3d390-96b8-432d-8acd-af64c0ad6636%2Fkfxx86_processed.png&w=3840&q=75)
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