Subject: Pre-Calculus 30
Outcome: P30.11 - Demonstrate understanding of radical and rational functions with restrictions on the
domain.
Beginning – 1
Approaching – 2
Proficiency – 3
Mastery – 4
I need help.
I have a basic understanding.
My work consistently meets
expectations.
I have a deeper understanding.
With assistance, I can apply
transformations to sketch the graph
of a radical and rational function and
compare the domain and range of
the two functions, with the use of
technology.
I can apply transformations to
sketch the graph of a radical and
rational function and compare the
domain and range of the two
functions, with the use of
technology.
I can apply transformations to
sketch the graph of a radical and
rational function and compare the
domain and range of the two
functions, without the use of
technology.
I can create the equation for a
radical function and a rational
function from a graph.
I can determine where a rational
function has an asymptote or hole,
without technology.
Indicators – please select and assess as appropriate to your unit, bold text indicates possible key indicators.
a.
Sketch the graph of the function y = √ x using a table of values, and state the domain and range of function.
b.
Develop, generalize, explain, and apply transformations to the function y = √x to sketch the graph of y - k = a√b(x - h) .
c.
Sketch the graph of the function y = √f(x) given the graph of the function y = f(x), and compare the domains and ranges of the two functions.
d.
Describe the relationship between the roots of a radical equation and the x-intercepts of the graph of the corresponding radical function.
e.
Determine, graphically, the approximate solutions to radical equations.
f.
Sketch rational functions, with and without the use of technology.
g.
Explain the behaviour (shape and location) of the graphs of rational functions for values for the dependent variable close to the location of a vertical asymptote.
h.
Analyze the equation of a rational function to determine where the graph of the rational function has an asymptote or a hole, and explain why.
i.
Match a set of equations for rational and radical functions to their corresponding graphs.
j.
Describe the relationship between the roots of a rational equation and the x-intercepts of the graph of the corresponding rational function.
k.
Determine graphically an approximate solution to a rational equation.
l.
Critique statements such as “Any value that makes the denominator of a rational function equal to zero will result in a vertical asymptote on the graph of the rational
function”.
Refer to the Saskatchewan Curriculum Guide Pre-Calculus 30