Use the X-Intercepts to Find the Intervals on Which the Graph

question 88

Multiple Choice

Use the x-intercepts to find the intervals on which the graph of f is above and below the x-axis.
- $$f ( x ) = \left( x + \frac { 1 } { 8 } \right) ^ { 2 } ( x - 2 ) ^ { 5 }$$

• A) above the \(x\)-axis: \(\left( - \frac { 1 } { 8 } , 2 \right)\)
• below the X-axis: \(\left( - \infty , - \frac { 1 } { 8 } \right) , ( 2 , \infty )\)
• B) above the \(x\)-axis: \(\left( - \infty , - \frac { 1 } { 8 } \right) , ( 2 , \infty )\)
• below the x-axis: \(\left( - \frac { 1 } { 8 } , 2 \right)\)
• C) above the \(x\)-axis: \(\left( - \infty , - \frac { 1 } { 8 } \right) , \left( - \frac { 1 } { 8 } , 2 \right)\)
• below the \(x\)-axis: \(( 2 , \infty )\)
• D) above the \(x\)-axis: \(( 2 , \infty )\)
• below the \(x\)-axis: \(\left( - \infty , - \frac { 1 } { 8 } \right) , \left( - \frac { 1 } { 8 } , 2 \right)\)

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Definitions:

Posterior Thigh

The back part of the thigh, comprising muscles like the hamstrings that are involved in extension of the hip and flexion of the knee.

Biceps Femoris

A muscle of the thigh that is part of the hamstring group, involved in knee flexion and thigh extension.

Tensor Fasciae Latae

A muscle of the thigh involved in stabilizing the hip and knee during movements.

Sternocleidomastoid

A neck muscle that facilitates the bending and turning of the head.