Download af(x) and f(bx) (Lucy McGuigan`s conflicted copy 2016-10

Warm Up – Monday 10/14/15 – CHOOSE THREE- Do on back of
WS #9
1. Given the function 𝑓 𝑥 = 3𝑥 − 1, evaluate 𝑓 −3
2. Convert -2x + 5y = -20 into slope-intercept form.
1
𝑥
2
3. Given the function 𝑔 𝑥 =
+ 5, evaluate 𝑔 2
4. Lyft charges an initial fee of $3.50 for a ride, plus $2.75 per mile driven.
Write an equation that gives the total cost, C, in terms of m, the miles
driven.
5. Which of the following describes the transformation from 𝑓 𝑥 to
𝑓 𝑥+2 ?
A. Horizontal shift two units to the left
B. Horizontal shift two units to the right
C. Vertical shift two units up
D. Vertical shift two units down
•Announcements:
• Classwork 1-7 due Tuesday,
October 18th
• HW was due Thursday
 Make sure to SHOW WORK
Tutoring
Morning
(8:05 – 8:40 AM)
Afternoon
(4:15 – 4:45 PM)
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
Mrs. Broden (2115)!
Goal
SWBAT determine the effects on a
linear parent function when f(x) is
replaced by af(x) and f(bx)
Our Goals This Week:
HW
90%
DOL
75%
Why This Matters
This allows us to figure out the effect of multiplying our
input vs. multiplying our output.
Example: Murray St. Café currently charges $1 per hour for
internet service with an initial fee of $0.75, but they are
planning to change their rates. They are considering
charging either (A) $1 per half hour, keeping the same initial
fee of $0.75, or (B) $0.80 per hour with an initial fee of
$0.60, reducing both the hourly fee and initial charge by
20%. Which of these options will earn them more money if
most customers use the internet for more than an hour?
Total charge (in dollars)
Murray St. Café currently charges $1
per hour for internet service with an
initial fee of $0.75, but they are
planning to change their rates. They
are considering charging either:
(A)$1 per half hour, keeping the
same initial fee of $0.75, or
(B)$0.80 per hour with an initial fee
of $0.60, reducing both the
hourly fee and initial charge by
20%.
Which of these options will earn
them more money if most
customers use the internet for
more than an hour?
Time on the internet (in hours)
-1
𝒇(𝒙)
4
𝟐𝒇(𝒙)
multiply
output / value of f(x) by that number
6
5
4
3
2
1
12
10
8
6
4
2
3
2.5
2
1.5
1
0.5
steeper
𝟏
𝒇(𝒙)
𝟐
-6
-5
-4
-3
-2
-1
all have same
x-intercept
less steep
−𝒇(𝒙)
mirror image
Both the slope and the y-intercept change!
numbers
Vertical
between 0 and 1
𝟏
stretched vertically by a factor of
𝒂
less steep
greater than 1
compressed vertically by a factor of a
steeper
reflected
x-axis
-1
2
multiply
𝒇(𝟐𝒙)
steeper
𝒇(𝒙)
𝟏
𝒙
𝟐
less steep
input / value of x
-5
-9
-3
-5
-1
1
3
5
-1
3
7
11
𝒇
for x = -2
Example:
-2 3 for Example:
x = -2
-3 for x =Example:
2(−𝑥)– 1
𝑓(2𝑥)= 2(2𝑥) –𝑓 1 1 𝑥 = 2 1 𝑥𝑓(−𝑥)=
–
1
2(−(−2))–
1 same
-22 (2(−2)) –2 11 1 2
all have
2 2 (−2) – 12(2)– 1
2(-4)– 1
y-intercept
-1 -9
3
-12(-1)– 1
Use original x-coordinate-3 Use original x-coordinate
0 y-coordinate
and new y-coordinate to
and new
to x-coordinate
Use -3
original
graph to
graph
and new y-coordinate
1
-5
graph
2
𝒇(−𝒙)
mirror image
-7
The slope changes, the y-intercept doesn’t!
numbers
Vertical
Horizontal
between 0 and 1
stretched vertically by a factor of
𝟏
𝒂
between 0 and 1
stretched horizontally by a factor of
less steep
less steep
greater than 1
greater than 1
compressed vertically by a factor of a
compressed horizontally by a factor of b
steeper
steeper
reflected
x-axis
𝟏
𝒃
reflected
y-axis
Independent Practice
•Directions
• Complete ALL problems except 4
• Silently and independently
• Check work at the board
Demonstration of Learning (10/14/2016)
1. Which of the following describes the transformation from 𝑓 𝑥 to 2𝑓 𝑥 ?
A.
B.
C.
D.
Horizontal stretch by a factor of 2, making it steeper
Horizontal compression by a factor of 2, making it steeper
Vertical stretch by a factor of 2, making it steeper
Vertical compression by a factor of 2, making it steeper
2. Which of the following describes the transformation from ℎ 𝑥 to ℎ
A.
B.
C.
D.
Horizontal stretch by a factor of 2 and reflection across the y-axis
Horizontal compression by a factor of 2 and reflection across the y-axis
Vertical stretch by a factor of 2 and reflection across the y-axis
Vertical compression by a factor of 2 and reflection across the x-axis
1
− 𝑥
2
?