Exploring Graphing Rational Functions and Transformations

What is the basic equation for a rational parent function?

• f(x) = x - 1

• f(x) = x + 1

• f(x) = 1/x

• f(x) = x^2

What is the name of the graph for rational functions?

• Hyperbola

• Ellipse

• Parabola

• Circle

What happens when you plot the points for the rational function f(x) = 1/x?

• The points form a circle

• The points are reflections of each other

• The points are random

• The points form a straight line

What is an asymptote in the context of rational functions?

• A point where the graph intersects the axis

• A line the graph gets close to but never touches

• A maximum point on the graph

• A minimum point on the graph

What is the domain of the function f(x) = 1/x?

• All positive numbers

• All negative numbers

• All real numbers except zero

• All real numbers

What is the range of the function f(x) = 1/x?

• All real numbers except zero

• All positive numbers

• All negative numbers

• All real numbers

What are the lines of symmetry for the rational function f(x) = 1/x?

• X = 1 and Y = 1

• X = -1 and Y = -1

• Y = X and Y = -X

• X-axis and Y-axis

What are the locator points for the rational function f(x) = 1/x?

• (3,3) and (-3,-3)

• (2,2) and (-2,-2)

• (1,1) and (-1,-1)

• (0,0)

What effect does the parameter 'a' have on the graph of a rational function?

• It rotates the graph

• It moves the graph left or right

• It stretches or shrinks the graph

• It moves the graph up or down

What happens to the graph of a rational function when 'a' is negative?

• The graph shifts left

• The graph shifts right

• The graph reflects over the vertical asymptote

• The graph reflects over the horizontal asymptote