A politician wants to estimate the proportion of constituents favouring a controversial piece of proposed legislation. Suppose t
1 answer:
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Answer:
Choice A) .
Step-by-step explanation:
What are the changes that would bring to
?
- Translate
to the left by
unit, and
- Stretch
. 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
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:
Step-by-step explanation:
There are 3 possibilities for the graph as shown in the figure.
(a) having zero intersection
(b) having one intersection point (touching point)
(c) having two intersection points.
So, the greatest possible number of intersections for these graphs is 2 as shown in figure (c).
