Pre-Calculus 30 Outcome 1a Assessment 1
2
30.7 & 30.8
Outcome 1a:
I can extend understanding
of transformations and
reflections to include
functions and inverses
(given in equation or graph
form) in general, including
horizontal and vertical
translations and stretches,
and reflections through the
x- axis, y-axis and line y=x.
3
4
I can identify the parameters a, b, h, and
k and describe their effect on the graph
of y=f(x) given the equation y=f(x)
I can describe and graph
combinations of transformations,
stretches, and reflections.
I can sketch functions with single
transformations, stretches, and
reflections of y = f(x) when given the
graph of y=f(x).
I can write the equation of functions
that has undergone specified
translations and or stretches from a
given function in the form y = a
f(b(x-h))+k
I can write equations of functions with
single transformations or reflections
through the x- axis, y-axis or y = x line.
I can develop and apply numeric,
algebraic, graphic strategies to
determine if two relations are
inverses of each other.
I can generalize about the effects of the
placement of different coefficients on the
original graph of y = f(x).
I can explain strategies to determine if a relation
and its inverse are functions
I can determine what restrictions must be placed
on domain of a function for its inverse to be a
function.
I made no errors.
Level 2
1.
Given the graph of y=f(x),
a) On the same graph, sketch the graph of the transformed function if it is translated 3
units right.
b) Write the equation of the transformed graph.
2.
For each equation of a translated image, describe how the graph of y=f(x) was
translated, reflected, or stretched.
a)
7
b)
3.
Determine an equation of the inverse of
3
Level 3
4.
Here is the graph of y=f(x).
a) On the same grid, sketch and label its image after a vertical stretch by a factor of 3,
and a translation of 4 units left and 2 units down.
b) Write the equation of the transformed image in the form y = a f(b(x-h))+k.
5.
Describe the graph of the second function as a transformation image of the graph of
the first function.
a)
2
5
3
b)
6.
4
Determine algebraically whether the functions are inverses of each other.
7
3 and
7. Determine whether the functions are inverses of each other. Justify you answer.
Level 4
8. a) Sketch the following function and its inverse on the same grid.
2
1
2
b) Is the inverse a function? Explain why or why not.
c) If the inverse is not a function, determine how to restrict the domain of the original
function so that the inverse is a function.