Mr Thauvette DP SL Mathematics Graphs of Functions The x intercepts of a function are the values of x for which y 0 They are the zeros ie solutions roots of the function ID: 425413
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Slide1
Functions and equations
Mr. Thauvette
DP SL MathematicsSlide2
Graphs of FunctionsThe x-intercepts of a function are the values of
x
for which
y = 0. They are the zeros (i.e., solutions, roots) of the function.
The
y
-intercept
of a function is the value of
y
when
x
= 0.Slide3
Graphs of Functions
An
asymptote
is a line that the graph approaches or begins to looklike as it tends to infinity in a particular direction.
v
ertical asymptote
horizontal asymptote
y
= 2
x
= 2Slide4
Graphs of FunctionsTo find vertical asymptotes, look for values of x for which the
f
unction is undefined:
If find where
If find where
To find horizontal asymptotes, consider the
behaviour
as Slide5
Transformations of Graphs translates
vertically units.
translates
horizontally units.
translates
by the vectorSlide6
translates vertically units.Slide7
translates vertically units.Slide8
translates vertically units.Slide9
translates vertically units.Slide10
ExamplesFind the equation of the relation under the translation vectorindicated. Graph both the original and translated relations on the
same set of axes.
(a) (b) Slide11
Example (a)Slide12
Example (a)Slide13
Example (b)Slide14
Example (b)Slide15
translates horizontally units.Slide16
translates horizontally units.Slide17
translates horizontally units.Slide18
translates horizontally units.Slide19
ExamplesFind the equation of the relation under the translation vectorindicated. Graph both the original and translated relations on the
same set of axes.
(a) (b) Slide20
Example (a)Slide21
Example (a)Slide22
Example (b)Slide23
Example (b)Slide24
SummarySlide25
translates by the vector
EXAMPLE:
Find the equation of under the translationSlide26
Find the equation of under the translationSlide27
Dilation from the x-axis is a
vertical stretch
of
with dilation factor .Slide28
Dilation from the x-axisSlide29
Dilation from the x-axisSlide30
Dilation from the x-axisSlide31
Dilation from the x-axisSlide32
Dilation from the x-axisSlide33
Dilation from the y-axis is a
horizontal stretch
of
with dilation factor .Slide34
Dilation from the y-axisSlide35
Dilation from the y-axisSlide36
Dilation from the y-axisSlide37
Dilation from the y-axisSlide38
Dilation from the y-axisSlide39
ReflectionsSlide40
Reflection about the x-axisSlide41
Reflection about the y-axis