Graphs of Functions in Mathematics
undefined
LO: To draw the graph of a function given its
equation.
The graph of a function, its
equation
y
=
f
(
x
)
30 September 2024
Sketching its graph.
In this lesson we will be working on Drawing the graph
of a function
If you are asked to draw the graph of a function is to
represent by means of a labelled, accurate diagram or
graph, using a pencil. A ruler (straight edge) should be
used for straight lines.
The graph of a function
Every function has a particular behaviour and is
identified by a specific shape.
There are two ways to represent the graph of a
function.
Drawing its graph.
Graphs should have points correctly plotted (if appropriate)
and joined in a straight line or smooth curve.
We can create a table of values that combines the inputs
and outputs
We will use values from -3
through 3 for
x
and from them,
we will evaluate the function to
find the corresponding value of
y
Draw the graph of
f
(
x
)
=
2
x
+ 1 for
– 3 ≤
x
≤ 3
.
-3
-2
-1
0
1
2
3
The graph of a function
(
-2
,
-3
)
(
-1
,
-1
)
(
0
,
1
)
(
1
,
3
)
(
2
,
5
)
-3
-1
1
3
5
-5
7
(
-3
,
-5
)
(
3
,
7
)
f
(
x
)
= 2
x
+ 1
Plot the points accurately.
Use a ruler to join the points.
We can create a table of values that combines the inputs
and outputs
We will use values from -3
through 3 for
x
and from them,
we will evaluate the function to
find the corresponding value of
y
Draw the graph of
f
(
x
)
=
x
2
–
1 for
– 3 ≤
x
≤ 3
.
-3
-2
-1
0
1
2
3
The graph of a function
(
-2
,
3
)
(
-1
,
0
)
(
0
,
-1
)
(
1
,
0
)
(
2
,
3
)
3
0
-1
0
3
8
8
(
-3
,
8
)
(
3
,
8
)
f
(
x
)
=
x
2
–
1
Plot the points accurately.
Draw a smooth curve joining the
points.
Using the GDC
We are going to use Graphing display calculator to generate the
table. Select the Calculator you are using.
CASIO
Texas Instruments
The graph of a function
We will use values from
–
2
through 3 for
x
and from them,
we will evaluate the function to
find the corresponding value of
y
-2
-1
0
1
2
3
The graph of a function
Now we are going to u
se the GDC
to construct a table of values for
–
2
≤
x
≤
3
.
Turn on the GDC.
Press 7
Table
We can create a table of values that combines the inputs
and outputs
Draw the graph of
f
(
x
)
=
x
3
–
x
2
– 7
x
–
1 for
– 2 ≤
x
≤ 3
.
-2
-1
0
1
2
3
The graph of a function
Type in the function
x
3
–
x
2
– 7
x
–
1
EXE
We can create a table of values that combines the inputs
and outputs
Draw the graph of
f
(
x
)
=
x
3
–
x
2
– 7
x
–
1 for
– 2 ≤
x
≤ 3
.
-2
-1
0
1
2
3
The graph of a function
Type in the function
x
3
–
x
2
– 7
x
–
1
Press F5
Set
EXE
We can create a table of values that combines the inputs
and outputs
Draw the graph of
f
(
x
)
=
x
3
–
x
2
– 7
x
–
1 for
– 2 ≤
x
≤ 3
.
-2
-1
0
1
2
3
The graph of a function
Type in the function
x
3
–
x
2
– 7
x
–
1
Press F5
Set
EXE
Set the boundaries
Start -2
End 3
EXE
EXE
Step 1
EXE
We can create a table of values that combines the inputs
and outputs
Draw the graph of
f
(
x
)
=
x
3
–
x
2
– 7
x
–
1 for
– 2 ≤
x
≤ 3
.
-2
-1
0
1
2
3
The graph of a function
Type in the function
x
3
–
x
2
– 7
x
–
1
Press F5
Set
EXE
Set the boundaries
Start -2
End 3
EXE
EXE
Step 1
EXE
Press F6
Table
We can create a table of values that combines the inputs
and outputs
Draw the graph of
f
(
x
)
=
x
3
–
x
2
– 7
x
–
1 for
– 2 ≤
x
≤ 3
.
-2
-1
0
1
2
3
The graph of a function
Type in the function
x
3
–
x
2
– 7
x
–
1
Press F5
Set
EXE
Set the boundaries
Start -2
End 3
EXE
EXE
Step 1
EXE
Press F6
Table
Scroll down and fill in the table
(
-2
,
1
)
(
-1
,
4
)
(
0
,
-1
)
(
1
,
-8
)
(
2
,
-11
)
1
4
-1
-8
-11
-4
(
3
,
-4
)
We can create a table of values that combines the inputs
and outputs
Draw the graph of
f
(
x
)
=
x
3
–
x
2
– 7
x
–
1 for
– 2 ≤
x
≤ 3
.
We can create a table of values that combines the inputs
and outputs
Draw the graph of
f
(
x
)
=
x
3
–
x
2
– 7
x
–
1 for
– 2 ≤
x
≤ 3
.
The graph of a function
Plot the points accurately.
Draw a smooth curve joining the
points.
-2
-1
0
1
2
3
(
-2
,
1
)
(
-1
,
4
)
(
0
,
-1
)
(
1
,
-8
)
(
2
,
-11
)
1
4
-1
-8
-11
-4
(
3
,
-4
)
f
(
x
)
=
x
3
–
x
2
– 7
x
–
1
Click to end
We will use values from
–
2
through 3 for
x
and from them,
we will evaluate the function to
find the corresponding value of
y
-2
-1
0
1
2
3
The graph of a function
Now we are going to u
se the GDC
to construct a table of values for
–
2
≤
x
≤
3
.
Turn on the GDC.
Press
Y =
We can create a table of values that combines the inputs
and outputs
Draw the graph of
f
(
x
)
=
x
3
–
x
2
– 7
x
–
1 for
– 2 ≤
x
≤ 3
.
-2
-1
0
1
2
3
The graph of a function
Type in the function
x
3
–
x
2
– 7
x
–
1
enter
We can create a table of values that combines the inputs
and outputs
Draw the graph of
f
(
x
)
=
x
3
–
x
2
– 7
x
–
1 for
– 2 ≤
x
≤ 3
.
-2
-1
0
1
2
3
The graph of a function
Type in the function
x
3
–
x
2
– 7
x
–
1
Press 2nd
tblset
enter
We can create a table of values that combines the inputs
and outputs
Draw the graph of
f
(
x
)
=
x
3
–
x
2
– 7
x
–
1 for
– 2 ≤
x
≤ 3
.
-2
-1
0
1
2
3
The graph of a function
Type in the function
x
3
–
x
2
– 7
x
–
1
Press F5
Set
EXE
Table Setup
TblStart = -2
æ
Tbl = 1
enter
enter
Indpnt: Auto
2nd
We can create a table of values that combines the inputs
and outputs
Draw the graph of
f
(
x
)
=
x
3
–
x
2
– 7
x
–
1 for
– 2 ≤
x
≤ 3
.
Depen: Auto
table
-2
-1
0
1
2
3
The graph of a function
Type in the function
x
3
–
x
2
– 7
x
–
1
Press F5
Set
EXE
We can create a table of values that combines the inputs
and outputs
Draw the graph of
f
(
x
)
=
x
3
–
x
2
– 7
x
–
1 for
– 2 ≤
x
≤ 3
.
Table Setup
TblStart = -2
æ
Tbl = 1
enter
enter
Indpnt: Auto
2nd
Depen: Auto
table
-2
-1
0
1
2
3
The graph of a function
Scroll down and fill in the table
(
-2
,
1
)
(
-1
,
4
)
(
0
,
-1
)
(
1
,
-8
)
(
2
,
-11
)
1
4
-1
-8
-11
-4
(
3
,
-4
)
We can create a table of values that combines the inputs
and outputs
Draw the graph of
f
(
x
)
=
x
3
–
x
2
– 7
x
–
1 for
– 2 ≤
x
≤ 3
.
We can create a table of values that combines the inputs
and outputs
Draw the graph of
f
(
x
)
=
x
3
–
x
2
– 7
x
–
1 for
– 2 ≤
x
≤ 3
.
The graph of a function
Plot the points accurately.
Draw a smooth curve joining the
points.
-2
-1
0
1
2
3
(
-2
,
1
)
(
-1
,
4
)
(
0
,
-1
)
(
1
,
-8
)
(
2
,
-11
)
1
4
-1
-8
-11
-4
(
3
,
-4
)
f
(
x
)
=
x
3
–
x
2
– 7
x
–
1
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info@mathssupport.org
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Learn how to draw the graph of a function using its equation. Explore examples such as plotting the graph of f(x) = 2x + 1 and f(x) = x^2 + 1 within specific ranges. Understand the process of creating tables of values, plotting points accurately, and connecting them with straight lines or smooth curves to represent functions graphically.
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Presentation Transcript
30 September 2024 The graph of a function, its equation y = f(x) LO: To draw the graph of a function given its equation. www.mathssupport.org
The graph of a function Every function has a particular behaviour and is identified by a specific shape. There are two ways to represent the graph of a function. Drawing its graph. Sketching its graph. In this lesson we will be working on Drawing the graph of a function If you are asked to draw the graph of a function is to represent by means of a labelled, accurate diagram or graph, using a pencil. A ruler (straight edge) should be used for straight lines. Graphs should have points correctly plotted (if appropriate) and joined in a straight line or smooth curve. www.mathssupport.org
The graph of a function Draw the graph of f(x) = 2x + 1 for 3 x 3. We can create a table of values that combines the inputs and outputs y 10 9 -3 -5 -2 -3 -1 -1 0 1 1 3 2 5 3 7 x 8 y = f(x) 7 (-2,-3)(-1,-1) (0, 1) (1, 3) (2, 5) (-3,-5) (3, 7) (x, y) 6 5 We will use values from -3 through 3 for x and from them, we will evaluate the function to find the corresponding value of y Plot the points accurately. Use a ruler to join the points. 4 3 f(x) = 2x + 1 2 1 x 1 2 3 4 5 6 6 5 4 3 2 1 -1 -2 -3 -4 -5 www.mathssupport.org
The graph of a function Draw the graph of f(x) = x2 1 for 3 x 3. We can create a table of values that combines the inputs and outputs y f(x) = x2 1 10 9 -3 8 -2 3 -1 0 0 -1 1 0 2 3 3 8 x 8 y = f(x) 7 (-3,8) (-2,3) (-1,0) (0, -1)(1, 0) (2, 3) (3, 8) (x, y) 6 5 We will use values from -3 through 3 for x and from them, we will evaluate the function to find the corresponding value of y Plot the points accurately. Draw a smooth curve joining the points. 4 3 2 1 x 1 2 3 4 5 6 6 5 4 3 2 1 -1 -2 -3 -4 -5 www.mathssupport.org
The graph of a function Using the GDC We are going to use Graphing display calculator to generate the table. Select the Calculator you are using. CASIO Texas Instruments CASIO Texas Instruments www.mathssupport.org
The graph of a function Draw the graph of f(x) = x3 x2 7x 1 for 2 x 3. We can create a table of values that combines the inputs and outputs -2 -1 0 1 2 3 x y = f(x) (x, y) We will use values from 2 through 3 for x and from them, we will evaluate the function to find the corresponding value of y Now we are going to use the GDC to construct a table of values for 2 x 3 .Turn on the GDC. Press 7 Table www.mathssupport.org
The graph of a function Draw the graph of f(x) = x3 x2 7x 1 for 2 x 3. We can create a table of values that combines the inputs and outputs -2 -1 0 1 2 3 x y = f(x) (x, y) Type in the function x3 x2 7x 1 EXE www.mathssupport.org
The graph of a function Draw the graph of f(x) = x3 x2 7x 1 for 2 x 3. We can create a table of values that combines the inputs and outputs -2 -1 0 1 2 3 x y = f(x) (x, y) EXE Type in the function x3 x2 7x 1 Press F5 Set www.mathssupport.org
The graph of a function Draw the graph of f(x) = x3 x2 7x 1 for 2 x 3. We can create a table of values that combines the inputs and outputs -2 -1 0 1 2 3 x y = f(x) (x, y) EXE Type in the function x3 x2 7x 1 Press F5 Set Set the boundaries Start -2 EXE EXE EXE End 3 Step 1 www.mathssupport.org
The graph of a function Draw the graph of f(x) = x3 x2 7x 1 for 2 x 3. We can create a table of values that combines the inputs and outputs -2 -1 0 1 2 3 x y = f(x) (x, y) EXE Type in the function x3 x2 7x 1 Press F5 Set Set the boundaries Start -2 EXE EXE EXE End 3 Step 1 Press F6 Table www.mathssupport.org
The graph of a function Draw the graph of f(x) = x3 x2 7x 1 for 2 x 3. We can create a table of values that combines the inputs and outputs -2 1 -1 4 0 -1 1 -8 2 3 x -11 -4 y = f(x) (-2,1) (-1,4) (0, -1)(1,-8)(2,-11) (3,-4) (x, y) EXE Type in the function x3 x2 7x 1 Press F5 Set Set the boundaries Start -2 EXE EXE EXE End 3 Step 1 Press F6 Table Scroll down and fill in the table www.mathssupport.org
The graph of a function Draw the graph of f(x) = x3 x2 7x 1 for 2 x 3. We can create a table of values that combines the inputs and outputs y 5 f(x) = x3 x2 7x 1 4 3 -2 1 -1 4 0 -1 1 -8 2 3 x 2 -11 -4 y = f(x) 1 x (-2,1) (-1,4) (0, -1)(1,-8)(2,-11) (3,-4) (x, y) 3 2 1 1 2 3 -1 Plot the points accurately. Draw a smooth curve joining the points. -2 -3 -4 -5 --6 -7 -8 -9 -10 -11 Click to end Click to end www.mathssupport.org
The graph of a function Draw the graph of f(x) = x3 x2 7x 1 for 2 x 3. We can create a table of values that combines the inputs and outputs -2 -1 0 1 2 3 x y = f(x) (x, y) We will use values from 2 through 3 for x and from them, we will evaluate the function to find the corresponding value of y Now we are going to use the GDC to construct a table of values for 2 x 3 .Turn on the GDC. Press Y = www.mathssupport.org
The graph of a function Draw the graph of f(x) = x3 x2 7x 1 for 2 x 3. We can create a table of values that combines the inputs and outputs -2 -1 0 1 2 3 x y = f(x) (x, y) Type in the function x3 x2 7x 1 enter www.mathssupport.org
The graph of a function Draw the graph of f(x) = x3 x2 7x 1 for 2 x 3. We can create a table of values that combines the inputs and outputs -2 -1 0 1 2 3 x y = f(x) (x, y) enter Type in the function x3 x2 7x 1 Press 2nd tblset www.mathssupport.org
The graph of a function Draw the graph of f(x) = x3 x2 7x 1 for 2 x 3. We can create a table of values that combines the inputs and outputs -2 -1 0 1 2 3 x y = f(x) (x, y) EXE Type in the function x3 x2 7x 1 Press F5 Set Table Setup enter TblStart = -2 Tbl = 1 enter Indpnt: Auto Depen: Auto table 2nd www.mathssupport.org
The graph of a function Draw the graph of f(x) = x3 x2 7x 1 for 2 x 3. We can create a table of values that combines the inputs and outputs -2 -1 0 1 2 3 x y = f(x) (x, y) EXE Type in the function x3 x2 7x 1 Press F5 Set Table Setup enter TblStart = -2 Tbl = 1 Indpnt: Auto Depen: Auto enter table 2nd www.mathssupport.org
The graph of a function Draw the graph of f(x) = x3 x2 7x 1 for 2 x 3. We can create a table of values that combines the inputs and outputs -2 1 -1 4 0 -1 1 -8 2 3 x -11 -4 y = f(x) (-2,1) (-1,4) (0, -1)(1,-8)(2,-11) (3,-4) (x, y) Scroll down and fill in the table www.mathssupport.org
The graph of a function Draw the graph of f(x) = x3 x2 7x 1 for 2 x 3. We can create a table of values that combines the inputs and outputs y 5 f(x) = x3 x2 7x 1 4 3 -2 1 -1 4 0 -1 1 -8 2 3 x 2 -11 -4 y = f(x) 1 x (-2,1) (-1,4) (0, -1)(1,-8)(2,-11) (3,-4) (x, y) 3 2 1 1 2 3 -1 Plot the points accurately. Draw a smooth curve joining the points. -2 -3 -4 -5 --6 -7 -8 -9 -10 -11 www.mathssupport.org
Thank you for using resources from A close up of a cage Description automatically generated For more resources visit our website https://www.mathssupport.org If you have a special request, drop us an email info@mathssupport.org Get 20% off in your next purchase from our website, just use this code when checkout: MSUPPORT_20 www.mathssupport.org
