Explain How the Graph Of $g ( x ) = \frac { | x + 1 | - 2 } { 3 }$

question 15

Multiple Choice

Explain how the graph of $g ( x ) = \frac { | x + 1 | - 2 } { 3 }$ is obtained from the graph of $f = | x |$ .

• A) Shift the graph of \(f\) one unit to the right, then shift downward
• \(\frac { 2 } { 3 }\) units.
• B) Shift the graph of \(f\) one unit to the right, then shift downward
• \(2\) units.
• C) Shift the graph of \(f\) one unit to the left, then shrink vertically by a factor of
• \(\frac { 2 } { 3 }\) .
• D) Shift the graph of \(f\) one unit to the left, then shift upward
• \(\frac { 2 } { 3 }\) units.
• E) Shift the graph of \(f\) one unit to the left, shrink vertically by a factor of
• \(\frac { 1 } { 3 }\) , shift downward
• \(\frac { 2 } { 3 }\) units.

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Definitions:

Z-statistic

A measure used in statistics to quantify the deviation of a data point or a group of data points from the mean, expressed in terms of standard deviations.

Two-tailed Test

A statistical test that allows for the exploration of relationships in both directions, enabling the detection of significant differences regardless of the direction.

Significant

Pertaining to results in statistical analysis, significant means the findings are unlikely to have occurred by chance and indicate a real effect or relationship.

Z-statistic

A statistical measure that quantifies the difference between a sample statistic and its population parameter, measured in units of the standard deviation.