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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