algebra 2 algebra 2 families of function vertical translations combining transformations its do by tomorrow

algebra 2 algebra 2 families of function vertical translations combining transformations please help its do by tomorrow fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff

VERB The Spanish teacher helped the town mayor
3. Complete the graphic organizer below.
Transformations
translation
translation
k units,
y = f(x) + k,
k units,
y = f(x) – K,
k>O
h units,
y = f(x – h),
h> 0
h units,
y = f(x + h).
h> 0
k> 0
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2
Problem Vertical Translation
Got sore the functions and y2 – 3 related? How are their
5. Draw the graphs on the coordinate plane below.
graphs related
4. Complete the above
– 2-3
5
4
3
2
1
х
1 2 3 4 5
-5-4-3-2-19
2
-3
-4
2
5
5
6. Write T for true or F for false.
for y = 2x.
Each output value for y = 2x – 3 is three less than the corresponding output value
The graph of y = 2x – 3 is the graph of y = 2x stretched vertically two units.
The graph of y = 2x – 3 is the graph of y
· 2x translated down three units.
The graphs of y = 2x – 3 and y = 2x are parallel.
Problem 2 Horizontal Translation
Airplane Altitud
U Dy Pearson Education, Inc. or its affiliates. All Rights Reserved
Got It? The graph shows the projected altitude f(x) of an airplane scheduled
to depart an airport at noon. If the plane leaves 30 minutes early, what function
represents this transformation?
21
f(x)
7. Circle the graph below that shows the plane leaving 30 minutes early,
15
Airplane Altitude
Airplane Altitude
Airplane Altitude
Altitude
(thousands of feet)
21
21
21
15
3
0
15
15
Altitude
(thousands of feet)
Altitude
(thousands of feet)
9
Altitude
(thousands of feet)
2 4
Hours After No
>
3
0
3
0
0
2 4
Hours After Noon
mon
0
2
4
Hours After Noon
0 2
Hours After Noon
47
Problem 3 Reflecting a Function Algebraically
Got It? Let h(x) be the reflection of f(x) = 3x + 3 in the x-axis. What is a function
rule for h(x)?
9. Circle the function that shows f(x) reflected in the x-axis.
f(-x)
-f(x)
10. Write the function rule for h(x) below. Then graph h(x) and f(x) to check
the reflection
4
3
2
-4-3-2-10
Problem 4 Stretch and Compression
Got It? For the function f(x) in the table below, what are the corresponding table
and graph for the transformation h(x) =)
11. Complete the table of output values 12. Graph on the coordinate plane below
-5
2
-2
2
0
-3
3
Problem 5 Combining Transformations
Got It? The function f(x) = x. The graph of g(x) is f(x) stretched vertically by a
factor of 2 and translated down 3 units. What is the function rule for g(x)?
13. Underline the correct word or expression to complete each sentence.
The function f(x) = x stretched vertically by a factor of 2 is
x + 2/X – 2 /2x/ -2x .
The function f(x) = x stretched vertically by a factor of 2 and then translated
down 3 units is – 2x + 3 / 2x – 3/ -2x – 3/ 2x + 3.
14. The function rule for the combined transformation is
Lesson Check
Do you UNDERSTAND?
Compare and Contrast The graph below shows f(x) = 0.5x – 1. Graph g(x)
by translating f(x) up 2 units and then stretching it vertically by a factor of 2.
Graph h(x) by stretching f(x) by a factor of 2 and then translating it up 2 units.
Compare the graphs of g(x) and h(x).
15. Graph g(x) and h(x).
16. Underline the correct word(s
complete each sentence or e
factor of 2
13. Underline the correct word
The function f(x) = x stretched vertically by a factor of T 15
*+ 2/3 – 2/2r/ -2r.
The function f(x) = x stretched vertically by a factor of 2 and then translated
down 3 units is – 2x + 3/2x – 37 -2x – 3/2x + 3.
14. The function rule for the combined transformation is
Lesson Check
Do you UNDERSTAND?
Compare and Contrast The graph below shows f(x) = 0.5x
1. Graph g(x)
by translating S(x) up 2 units and then stretching it vertically by a factor of 2.
Graph h(x) by stretching f(x) by a factor of 2 and then translating it up 2 units.
Compare the graphs of g(x) and h(x).
15. Graph g(x) and h(x).
16. Underline the correct word(s) or expression to
complete each sentence or equation.
у
5
g(x) and h(x) are / are not the same function.
4
3
g(x) = x + 2 / x – 2/x/ – x
1
х
h(x) = x + 2 / x – 2 / */ – X
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f(x)=0.5x – 1
-2.
g(x) and h(x) are
the same / parallel / perpendicular lines.
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