Understanding Rational Functions

The video tutorial explains how to analyze a rational function, f(x) = 1/(x+4) - 5, by determining its domain, range, vertical and horizontal asymptotes. The domain excludes x = -4 due to division by zero. The vertical asymptote is at x = -4, and the horizontal asymptote is y = -5. The range excludes y = -5. The tutorial uses a graphing calculator to visualize these concepts and concludes with a graph sketch.

What is the domain of the function f(x) = 1/(x+4) - 5?

• All real numbers except x = 0

• All real numbers

• All real numbers except x = 4

• All real numbers except x = -4

Why is x = -4 excluded from the domain of the function?

• It makes the denominator zero

• It makes the numerator zero

• It makes the function undefined

• It makes both numerator and denominator zero

What is a vertical asymptote in the context of this function?

• A point where the graph crosses the y-axis

• A line the graph approaches but never crosses

• A point where the graph crosses the x-axis

• A line the graph never touches

At which x-value does the vertical asymptote occur for the function f(x) = 1/(x+4) - 5?

• x = 4

• x = -4

• x = 0

• x = 5

What tool is used to graph the function and identify the vertical asymptote?

• A ruler

• A graphing calculator

• A protractor

• A compass

What is the horizontal asymptote of the function f(x) = 1/(x+4) - 5?

• y = -5

• y = -4

• y = 0

• y = 5

As x approaches infinity, what value does f(x) approach?

• 0

• 5

• -4

• -5

Why is y = -5 not included in the range of the function?

• The function never reaches this value

• The function is undefined at this value

• The function crosses this value

• The function is zero at this value

What is the range of the function f(x) = 1/(x+4) - 5?

• All real numbers except y = 0

• All real numbers except y = 5

• All real numbers except y = -5

• All real numbers

What happens to the fraction 1/(x+4) as x approaches infinity?

• It approaches 1

• It approaches -1

• It approaches 0

• It approaches infinity