Unit 1 Transformations & Conics
Unit 1 Lesson 5: Reflections
Reflection over the x-axis:
The graph of [pic] is shown
below.
Write an equation that Sketch the graph of
represents [pic] [pic] on the grid
below. (Use your
calculator.)
[pic]
Rule: Function Notation:
Mapping Notation:
Reflection over the y-axis:
The graph of [pic] is shown below.
Write an equation that Sketch the graph of
represents [pic] [pic] on the grid
below. (Use your
calculator.)
[pic]
Rule: Function Notation:
Mapping Notation:
Reflection over the line [pic]:
The graph of [pic] is shown below.
Write an equation that Sketch the graph of
represents [pic] [pic] on the grid
or [pic] (inverse) below. (Use your
calculator.)
[pic]
Rule: Function Notation:
Mapping Notation:
**When to use:
[pic] [pic]
In general:
If [pic] is transformed into
[pic]
[pic] [pic] or
[pic]
The graph is The graph is The graph is
reflected reflected reflected
over the over the over the
________ ________ ________
Ex) In each case below sketch the indicated
reflection given the graph of [pic].
a) [pic] b) [pic] c) [pic]
[pic] [pic] [pic]
Ex) Sketch the reflection indicated for each case
below given the graph of [pic].
a) [pic] b) [pic] c) [pic]
[pic] [pic] [pic]
Ex) If the graph of [pic] is indicated by the thin
line graph, write an equation that represents
each transformation (thick line graph) in terms
of [pic].
a) b) c)
[pic] [pic] [pic]
Ex) If [pic], write an equation for each of
the following.
a) [pic] b) [pic] c) [pic]
Sketch the graphs for each of the following.
[pic]
[pic]
[pic] [pic] [pic]
[pic][pic][pic]
Ex) Consider the function [pic].
a) Graph the function [pic] and its inverse.
[pic]
b) Is the inverse of [pic] a function? Explain how you can tell.
c) If the inverse is not a function, how can the domain of [pic]be restricted so that the inverse of [pic] is a function?
Reflections Assignment:
1) Sketch the reflection of each graph in the x-axis and then determine the equation of the reflected image.
a) [pic] b) [pic] c) [pic]
[pic] [pic] [pic]
2) Sketch the reflection of each graph in the y-axis and then determine the equation of the reflected image.
a) [pic] b) [pic] c) [pic]
[pic] [pic] [pic]
3) Use mapping notation to describe how the graph of each function can be found from the graph of the function [pic].
a) [pic] b) [pic] c) [pic]
4) Determine the zeros of the function [pic] after each transformation.
a) [pic] b) [pic]
5) The graph of a function [pic] is contained completely in the third quadrant. Identify in which quadrant the graph will be in after each transformation.
a) [pic] b) [pic] c) [pic] d)[pic]
6) Given the graph of [pic] below, identify the coordinates of the invariant point after each transformation.
[pic]
a) [pic] b) [pic] c) [pic]
7) Given the graph of each relation below, sketch the graph of its inverse.
a) b)
[pic] [pic]
8) For each function below, determine the equation of its inverse.
a) [pic] b) [pic]
9) For each case below, identify a restriction that can be placed on the domain of [pic] so that its inverse is also a function.
a) [pic] b) [pic]
10) The function for converting the temperature from degrees Fahrenheit, x, to degrees Celsius ,y, is [pic].
a) Determine the equivalent temperature in degrees Celsius for [pic]F.
b) Determine the inverse of this function. What does it represent? What do the variables represent?
c) Determine the equivalent temperature in degrees Fahrenheit for [pic]C.
d) If both functions were to be graphed, what does the invariant point represent in this situation?
Answers
Reflections Assignment:
1. a) [pic] b) [pic] c) [pic]
[pic] [pic] [pic]
2. a) [pic] b) [pic] c) [pic]
[pic] [pic] [pic]
3. a) [pic] b) [pic] c) [pic]
4. a) [pic], 3 b) [pic], 4
5. a) 2 b) 4 c) 3 d) 1
6. a) [pic] b) [pic] c) [pic]
7. a) b)
[pic] [pic]
8. a) [pic] b) [pic]
9. a) [pic] b) [pic]
10. a) [pic]C b) [pic] y represents the temperature in Fahrenheit and x represents the temperature in Celsius c) [pic]F
d) The invariant point represents where the temperature in Celsius means the same thing in Fahrenheit.
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