Answer:
Choice A)
.
Step-by-step explanation:
What are the changes that would bring
to
?
- Translate
to the left by
unit, and - Stretch
vertically (by a factor greater than
.)
. The choices of
listed here are related to
:
- Choice A)
; - Choice B)
; - Choice C)
; - Choice D)
.
The expression in the braces (for example
as in
) is the independent variable.
To shift a function on a cartesian plane to the left by
units, add
to its independent variable. Think about how
, which is to the left of
, will yield the same function value.
Conversely, to shift a function on a cartesian plane to the right by
units, subtract
from its independent variable.
For example,
is
unit to the left of
. Conversely,
is
unit to the right of
. The new function is to the left of
. Meaning that
should should add
to (rather than subtract
from) the independent variable of
. That rules out choice B) and D).
- Multiplying a function by a number that is greater than one will stretch its graph vertically.
- Multiplying a function by a number that is between zero and one will compress its graph vertically.
- Multiplying a function by a number that is between
and zero will flip its graph about the
-axis. Doing so will also compress the graph vertically. - Multiplying a function by a number that is less than
will flip its graph about the
-axis. Doing so will also stretch the graph vertically.
The graph of
is stretched vertically. However, similarly to the graph of this graph
, the graph of
increases as
increases. In other words, the graph of
isn't flipped about the
-axis.
should have been multiplied by a number that is greater than one. That rules out choice C) and D).
Overall, only choice A) meets the requirements.
Since the plot in the question also came with a couple of gridlines, see if the points
's that are on the graph of
fit into the expression
.
Answer:
6 square feet
Step-by-step explanation:
Carpet has w= 8 ft and l = 12 ft
Reduced carpet has w' = 2 ft
<u>Reduction factor is </u>
<u>Then </u>
<u>Area of small carpet</u>
Factors of 56 are: 1, 2, 4, 7, 8, 14, 28, 56
<span>Factors of 84 are: 1, 2, 3, 4, 6, 7, 12, 14, 21, </span>28, 42, 84
The outside term multiplies by the outside term on the oposite side to equal the answer.
Example:
Look at the factors of 84
84X1=84
2X42=84
3X28=84
and so on!
Answer:
18r
Step-by-step explanation:
Multiply 9 by 2