Pre-Cal Make up Exam 12/11

Front

What is the equation of the midline of a sinusoidal graph?

Back

The midline is the horizontal line that runs through the middle of the graph, typically represented as y = k, where k is the vertical shift of the function.

Front

What is a hole in a function?

Back

A hole occurs in a function at a specific x-value where the function is not defined, often due to a factor that cancels out in the function's expression.

Front

How do you find the horizontal asymptote of a rational function?

Back

The horizontal asymptote can be found by comparing the degrees of the numerator and denominator. If the degree of the numerator is less than the denominator, y = 0; if they are equal, y = leading coefficient of numerator / leading coefficient of denominator.

Front

What is a vertical asymptote?

Back

A vertical asymptote occurs at x-values where the function approaches infinity, typically where the denominator of a rational function equals zero.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

What does it mean for a function to be continuous?

Back

A function is continuous if there are no breaks, holes, or jumps in its graph, meaning it can be drawn without lifting the pencil.

Front

What is the difference between a removable and non-removable discontinuity?

Back

A removable discontinuity occurs at a point where a function is not defined but can be 'fixed' by redefining the function at that point. A non-removable discontinuity cannot be 'fixed' and typically occurs at vertical asymptotes.

Front

What is the significance of the leading coefficient in a polynomial function?

Back

The leading coefficient determines the end behavior of the polynomial function and influences the shape of its graph.

Front

How do you determine if a function is even, odd, or neither?

Back

A function is even if f(-x) = f(x), odd if f(-x) = -f(x), and neither if it does not satisfy either condition.