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Advfunc hw6

1. The document discusses functions and transformations. It provides examples of different types of transformations including translations, reflections, stretches, and compressions. It asks students to identify these transformations in function notation and sketch graphs showing the effects of transformations on base functions. 2. Students are asked to determine if relations represent functions using the vertical line test or other reasoning. They must also find the domain and range of functions. Examples include evaluating functions, finding intercepts, and stating domains and ranges of original and transformed functions. 3. The final questions involve transformations of exponential functions, including describing and sketching graphs resulting from combinations of stretches, compressions, and reflections applied to base exponential functions.

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Bryce Fields
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46 views3 pages

Advfunc hw6

1. The document discusses functions and transformations. It provides examples of different types of transformations including translations, reflections, stretches, and compressions. It asks students to identify these transformations in function notation and sketch graphs showing the effects of transformations on base functions. 2. Students are asked to determine if relations represent functions using the vertical line test or other reasoning. They must also find the domain and range of functions. Examples include evaluating functions, finding intercepts, and stating domains and ranges of original and transformed functions. 3. The final questions involve transformations of exponential functions, including describing and sketching graphs resulting from combinations of stretches, compressions, and reflections applied to base exponential functions.

Uploaded by

Bryce Fields
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Functions and Transformations

MCR 3UI UNIT 3: Review for Quiz

1. Circle the number of the transformation in function notation (see below) that matches
the description of the transformations (a) – (e).

a) f x  translated right 3 1 2 3 4 5 6 7 8
b) f x  translated up 3 1 2 3 4 5 6 7 8
c) f x  translated
down 3 and right 2 1 2 3 4 5 6 7 8
d) f x  translated
down 3 and left 2 1 2 3 4 5 6 7 8
e) f x  reflected in the y-axis 1 2 3 4 5 6 7 8
f) f x  reflected in the x-axis 1 2 3 4 5 6 7 8

1. y  f  x  2. y  f x  3. y  f x  3 4. y  f x  3
5. y  f x   3 6. y  f x  2  3 7. y  f x  2  3 8. y  f x  3  2

2. State whether each relation below represents a function. Explain your reasoning.
(Vertical line test is ONLY a valid reason if you provide a graph)
Also, determine the domain and range for each relation.

a) (1, 2), (2, 3), (2, 1), (4, 1) b) y  x c) x = -5 d) y = 7


□ Is a function □ Is a function □ Is a function □ Is a function
□ Is not a function □ Is not a function □ Is not a function □ Is not a function
Reasoning: Reasoning: Reasoning: Reasoning:

d) x 2  y 2  49 e) y  (x  3)2  4 f) f x   x  1
□ Is a function □ Is a function □ Is a function
□ Is not a function □ Is not a function □ Is not a function
Reasoning: Reasoning: Reasoning:

3. Given f x   5  4x , find
a) f(2) b) -f(3) c) x when f(x) = 10
4. Let f x   x  1
a) Determine the new image equation if y  f x  2  4 .

b) Sketch a graph of f x   x  1 and y  f x  2  4 on the same grid.


Label each curve.

c) State the domain and range of the


original image, f x   x  1 and
the transformed image,
y  f x  2  4 .

Original Image
D: {________________}
R: {________________}

Transformed Image
D: {________________}
R: {________________}

d) If the original image, f x   x  1 was transformed to y  f  x  state its


new domain and range.
D: {____________________} R: {____________________}

5. If f x  
1
 5, state the domain, range and the equations of the asymptotes.
x2
Vertical Asymptote: _____________ Horizontal Asymptote: _____________

D: {____________________} R: {____________________}
1

MCR3UI - Unit 5 Day 4

Transformation of Exponential Functions:


Stretches, Compressions Combinations

Practice Questions

1. Describe the transformations that maps the function y = 8x onto each function given.

(a) y = 21 8x


(b) y = 84x
(c) y = −8x
(d) y = 8−2x

2. Sketch the graph of each function in question 1. Use the graph of y = 8x as the base.

3. Write the equation for the function that results from each transformation applied to
the base function y = 7x

(a) reflect in the x-axis


(b) stretch vertically by a factor of 3
(c) stretch horizontally by a factor of 2.4
(d) reflect in the y-axis and compress vertically by a factor of 7

4. Describe the transformations and sketch the graph of y = − 21 2x−4 by using y = 2x




as the base and applying transformations.

5. Describe the transformations and sketch the graph of y = 3−0.5x−1 − 5 by using y = 3x


as the base and applying transformations.
 1 (x+3)
6. (a) Graph the function f (x) = 12 2 − 1 using transformations.
(b) Identify the following properties.
(i) domain
(ii) range
(iii) equation of the asymptote

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