Determine Whether the Given Function Is Continuous $y = \frac { 8 x - 7 } { x ^ { 2 } + 36 }$

question 67

Multiple Choice

Determine whether the given function is continuous. If it is not, identify where it is discontinuous and which condition fails to hold. You can verify your conclusions by graphing the function with a graphing utility, if one is available. $y = \frac { 8 x - 7 } { x ^ { 2 } + 36 }$

• A)discontinuous at \(x = - 36\)
• B)discontinuous at \(x = 6\)
• C)discontinuous at \(x = - 6\)
• D)discontinuous at \(x = 36\)
• E)continuous everywhere

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Definitions:

Dependent Variable

A variable in an experiment or model that is expected to change in response to changes in independent variables.

Perfect Correlation

Perfect correlation occurs when two variables move in unison, either directly (perfect positive correlation) or inversely (perfect negative correlation), with a correlation coefficient of +1 or -1, respectively.

Perfect Prediction

A situation where a model or analysis predicts the outcome with 100% accuracy, with no errors.

Regression Equation

An equation that describes the line of best fit through a dataset, used to predict the outcome variable.