b) I can determine the equation of each of the 19 basic functions given the graph of the
function.
c) I can determine domain, range, symmetry, even/odd, and points of discontinuity of basic
functions as well as the domain of more complex rational functions & radical functions.
d) I can determine the x-intercepts/roots/zeros/real solutions of translated basic functions if
they exist.
e) I can graph and construct equations of all of the 19 basic functions including when the
graph includes horizontal/phase shifts to the right or left, vertical shifts up or down, reflections
over x-axis, reflections over y-axis, and vertical stretches or compressions.
f) I can, given the graph, construct an equation of each of the 19 basic functions when it has
been horizontally / phase shifted to the right or left, vertically shifted up or down, reflected
over x-axis, reflected over y-axis, or stretched or compressed vertically.
g) I can, when given the graph of a function, determine its domain (including writing domain
in interval notation) and range (including writing range in interval notation).
h) I can, when given the graph of a function, determine its symmetry: y-axis, origin, or neither
and how symmetry relates to it being even or odd.
i) I can, when given the graph of a function, determine its local maximum, local minimum,
absolute maximum and absolute minimum.
j) I can, when given the graph of a function, determine intervals where the function is
increasing, decreasing, & constant (interval notation).
k) I can, when given the graph of a function, determine intervals where f(x) >0 or f(x) <0.
l) I can determine the domain of a function given an equation by acknowledging where a
m) function’s domain is not defined over the real numbers by looking for negative numbers
under square root, looking for values that make the denominator zero, looking for the logarithm
of positive numbers, and by looking for asymptotes of the trig functions .
n) I can analyze piecewise functions given the equation.
o) I can construct an equation of a piecewise function given the graph (equation and domain).
p) I can determine given values of piecewise functions.
q) I can create and apply piece-wise functions in order to evaluate real world problems.
r) I can evaluate a function at different x-values & will demonstrate the ability to evaluate the
difference quotient used in the definition of a derivative.
s) I can use the max/min feature on my calculator to determine intervals where the function is
increasing, decreasing, and constant.
5. Construct Graphs, Analyze, and Evaluate Polynomial functions.
a) I can discuss the characteristics of polynomial functions and be able to explain why a graph
is not a polynomial.
b) I can determine the number of real roots based on the number of times a polynomial crosses
or bounces off the x-axis
c) I can determine the number of imaginary roots based on non-uniform “wiggles” in the
graph.
d) I understand that piercing the x-axis results in an odd number of roots and that touching but
not piercing the x-axis results in an even number of roots.
e) I can determine the domain and range of a polynomial given its graph.
f) I can determine the number of roots of a polynomial given its equation.
g) I can determine the direction a graph is going as it moves to the left and the right based on
the degree of the polynomial & the lead coefficient’s positivity/negativity.