Mixing
A family of functions graphing
$begingroup$
(1.) A family of functions is given. Graph all the given members of the family in the viewing rectangles indicated.
f(x) = (x − c)^2
$$c = 1, -1, 3, -3; [−5, 5] times [−10, 10]$$
(2.) A family of functions is given. Graph all the given members of the family in the viewing rectangles indicated.
f(x) = cx^2
$$c = 1, 1/2, 2, −1, −2;[−5, 5] times [−10, 10]$$
Please explain how I would graph these.
algebra-precalculus
edited Sep 16 '14 at 2:28
MPW
29.9k12056
asked Sep 16 '14 at 2:08
KissamerKissamer
1115
$endgroup$
|
show 2 more comments
$begingroup$
(1.) A family of functions is given. Graph all the given members of the family in the viewing rectangles indicated.
f(x) = (x − c)^2
$$c = 1, -1, 3, -3; [−5, 5] times [−10, 10]$$
(2.) A family of functions is given. Graph all the given members of the family in the viewing rectangles indicated.
f(x) = cx^2
$$c = 1, 1/2, 2, −1, −2;[−5, 5] times [−10, 10]$$
Please explain how I would graph these.
algebra-precalculus
edited Sep 16 '14 at 2:28
MPW
29.9k12056
asked Sep 16 '14 at 2:08
KissamerKissamer
1115
$endgroup$
$begingroup$
Let me ask this. Do you know how the value of $c$ affects the shape of the graph for each of these examples?
$endgroup$
– MPW
Sep 16 '14 at 2:25
$begingroup$
Honestly, no. Please explain
$endgroup$
– Kissamer
Sep 16 '14 at 2:34
$begingroup$
I just posted an answer/hint. Please read it and let me know if you can understand what I mean.
$endgroup$
– MPW
Sep 16 '14 at 2:36
$begingroup$
Ok, so the values would would be substituted in c in f(x) = (x-c)^2?
$endgroup$
– Kissamer
Sep 16 '14 at 2:56
1
$begingroup$
Each value of $c$ defines a different function, and each one has a different graph. The graphs are all similar, but somewhat different. The point of the problem is for you to understand how the particular form makes the functions graph change as $c$ changes. In every case, the graph is a parabola, but in (1) the various parabolas are shifted horizontally by $c$ units, and in (2) the parabolas are stretched vertically by a factor of $c$. Fix the given value of $c$, make a table for $x$-values in $[-5,5]$, and plot the points. You should see it.
$endgroup$
– MPW
Sep 16 '14 at 4:57
|
show 2 more comments
$begingroup$
(1.) A family of functions is given. Graph all the given members of the family in the viewing rectangles indicated.
f(x) = (x − c)^2
$$c = 1, -1, 3, -3; [−5, 5] times [−10, 10]$$
(2.) A family of functions is given. Graph all the given members of the family in the viewing rectangles indicated.
f(x) = cx^2
$$c = 1, 1/2, 2, −1, −2;[−5, 5] times [−10, 10]$$
Please explain how I would graph these.
algebra-precalculus
edited Sep 16 '14 at 2:28
MPW
29.9k12056
asked Sep 16 '14 at 2:08
KissamerKissamer
1115
$endgroup$
(1.) A family of functions is given. Graph all the given members of the family in the viewing rectangles indicated.
f(x) = (x − c)^2
$$c = 1, -1, 3, -3; [−5, 5] times [−10, 10]$$
(2.) A family of functions is given. Graph all the given members of the family in the viewing rectangles indicated.
f(x) = cx^2
$$c = 1, 1/2, 2, −1, −2;[−5, 5] times [−10, 10]$$
Please explain how I would graph these.
algebra-precalculus
algebra-precalculus
edited Sep 16 '14 at 2:28
MPW
29.9k12056
asked Sep 16 '14 at 2:08
KissamerKissamer
1115
edited Sep 16 '14 at 2:28
MPW
29.9k12056
asked Sep 16 '14 at 2:08
KissamerKissamer
1115
edited Sep 16 '14 at 2:28
MPW
29.9k12056
edited Sep 16 '14 at 2:28
MPW
29.9k12056
edited Sep 16 '14 at 2:28
MPW
29.9k12056
29.9k12056
asked Sep 16 '14 at 2:08
KissamerKissamer
1115
asked Sep 16 '14 at 2:08
KissamerKissamer
1115
asked Sep 16 '14 at 2:08
KissamerKissamer
1115
1115
$begingroup$
Let me ask this. Do you know how the value of $c$ affects the shape of the graph for each of these examples?
$endgroup$
– MPW
Sep 16 '14 at 2:25
$begingroup$
Honestly, no. Please explain
$endgroup$
– Kissamer
Sep 16 '14 at 2:34
$begingroup$
I just posted an answer/hint. Please read it and let me know if you can understand what I mean.
$endgroup$
– MPW
Sep 16 '14 at 2:36
$begingroup$
Ok, so the values would would be substituted in c in f(x) = (x-c)^2?
$endgroup$
– Kissamer
Sep 16 '14 at 2:56
1
$begingroup$
Each value of $c$ defines a different function, and each one has a different graph. The graphs are all similar, but somewhat different. The point of the problem is for you to understand how the particular form makes the functions graph change as $c$ changes. In every case, the graph is a parabola, but in (1) the various parabolas are shifted horizontally by $c$ units, and in (2) the parabolas are stretched vertically by a factor of $c$. Fix the given value of $c$, make a table for $x$-values in $[-5,5]$, and plot the points. You should see it.
$endgroup$
– MPW
Sep 16 '14 at 4:57
|
show 2 more comments
$begingroup$
Let me ask this. Do you know how the value of $c$ affects the shape of the graph for each of these examples?
$endgroup$
– MPW
Sep 16 '14 at 2:25
$begingroup$
Honestly, no. Please explain
$endgroup$
– Kissamer
Sep 16 '14 at 2:34
$begingroup$
I just posted an answer/hint. Please read it and let me know if you can understand what I mean.
$endgroup$
– MPW
Sep 16 '14 at 2:36
$begingroup$
Ok, so the values would would be substituted in c in f(x) = (x-c)^2?
$endgroup$
– Kissamer
Sep 16 '14 at 2:56
1
$begingroup$
Each value of $c$ defines a different function, and each one has a different graph. The graphs are all similar, but somewhat different. The point of the problem is for you to understand how the particular form makes the functions graph change as $c$ changes. In every case, the graph is a parabola, but in (1) the various parabolas are shifted horizontally by $c$ units, and in (2) the parabolas are stretched vertically by a factor of $c$. Fix the given value of $c$, make a table for $x$-values in $[-5,5]$, and plot the points. You should see it.
$endgroup$
– MPW
Sep 16 '14 at 4:57
$begingroup$
Let me ask this. Do you know how the value of $c$ affects the shape of the graph for each of these examples?
$endgroup$
– MPW
Sep 16 '14 at 2:25
$begingroup$
Let me ask this. Do you know how the value of $c$ affects the shape of the graph for each of these examples?
$endgroup$
– MPW
Sep 16 '14 at 2:25
$begingroup$
Honestly, no. Please explain
$endgroup$
– Kissamer
Sep 16 '14 at 2:34
$begingroup$
Honestly, no. Please explain
$endgroup$
– Kissamer
Sep 16 '14 at 2:34
$begingroup$
I just posted an answer/hint. Please read it and let me know if you can understand what I mean.
$endgroup$
– MPW
Sep 16 '14 at 2:36
$begingroup$
I just posted an answer/hint. Please read it and let me know if you can understand what I mean.
$endgroup$
– MPW
Sep 16 '14 at 2:36
$begingroup$
Ok, so the values would would be substituted in c in f(x) = (x-c)^2?
$endgroup$
– Kissamer
Sep 16 '14 at 2:56
$begingroup$
Ok, so the values would would be substituted in c in f(x) = (x-c)^2?
$endgroup$
– Kissamer
Sep 16 '14 at 2:56
1
1
$begingroup$
Each value of $c$ defines a different function, and each one has a different graph. The graphs are all similar, but somewhat different. The point of the problem is for you to understand how the particular form makes the functions graph change as $c$ changes. In every case, the graph is a parabola, but in (1) the various parabolas are shifted horizontally by $c$ units, and in (2) the parabolas are stretched vertically by a factor of $c$. Fix the given value of $c$, make a table for $x$-values in $[-5,5]$, and plot the points. You should see it.
$endgroup$
– MPW
Sep 16 '14 at 4:57
$begingroup$
Each value of $c$ defines a different function, and each one has a different graph. The graphs are all similar, but somewhat different. The point of the problem is for you to understand how the particular form makes the functions graph change as $c$ changes. In every case, the graph is a parabola, but in (1) the various parabolas are shifted horizontally by $c$ units, and in (2) the parabolas are stretched vertically by a factor of $c$. Fix the given value of $c$, make a table for $x$-values in $[-5,5]$, and plot the points. You should see it.
$endgroup$
– MPW
Sep 16 '14 at 4:57
|
show 2 more comments
1 Answer
1
active
oldest
votes
$begingroup$
Huge Hints: For (1), it is generally true that $(x,y)$ lies on the graph of $y=f(x)$ exactly when $(x+c,y)$ lies on the graph of $y=f(x-c)$.
For (2), it is generally true that $(x,y)$ lies on the graph of $y=f(x)$ exactly when $(x,cy)$ lies on the graph of $y=cf(x)$.
In both cases, $f(x)=x^2$.
answered Sep 16 '14 at 2:35
MPWMPW
29.9k12056
$endgroup$
add a comment |
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1 Answer
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1 Answer
1
active
oldest
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active
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active
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$begingroup$
Huge Hints: For (1), it is generally true that $(x,y)$ lies on the graph of $y=f(x)$ exactly when $(x+c,y)$ lies on the graph of $y=f(x-c)$.
For (2), it is generally true that $(x,y)$ lies on the graph of $y=f(x)$ exactly when $(x,cy)$ lies on the graph of $y=cf(x)$.
In both cases, $f(x)=x^2$.
answered Sep 16 '14 at 2:35
MPWMPW
29.9k12056
$endgroup$
add a comment |
$begingroup$
Huge Hints: For (1), it is generally true that $(x,y)$ lies on the graph of $y=f(x)$ exactly when $(x+c,y)$ lies on the graph of $y=f(x-c)$.
For (2), it is generally true that $(x,y)$ lies on the graph of $y=f(x)$ exactly when $(x,cy)$ lies on the graph of $y=cf(x)$.
In both cases, $f(x)=x^2$.
answered Sep 16 '14 at 2:35
MPWMPW
29.9k12056
$endgroup$
add a comment |
$begingroup$
Huge Hints: For (1), it is generally true that $(x,y)$ lies on the graph of $y=f(x)$ exactly when $(x+c,y)$ lies on the graph of $y=f(x-c)$.
For (2), it is generally true that $(x,y)$ lies on the graph of $y=f(x)$ exactly when $(x,cy)$ lies on the graph of $y=cf(x)$.
In both cases, $f(x)=x^2$.
answered Sep 16 '14 at 2:35
MPWMPW
29.9k12056
$endgroup$
Huge Hints: For (1), it is generally true that $(x,y)$ lies on the graph of $y=f(x)$ exactly when $(x+c,y)$ lies on the graph of $y=f(x-c)$.
For (2), it is generally true that $(x,y)$ lies on the graph of $y=f(x)$ exactly when $(x,cy)$ lies on the graph of $y=cf(x)$.
In both cases, $f(x)=x^2$.
answered Sep 16 '14 at 2:35
MPWMPW
29.9k12056
answered Sep 16 '14 at 2:35
MPWMPW
29.9k12056
answered Sep 16 '14 at 2:35
MPWMPW
29.9k12056
answered Sep 16 '14 at 2:35
MPWMPW
29.9k12056
29.9k12056
add a comment |
add a comment |
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$begingroup$
Let me ask this. Do you know how the value of $c$ affects the shape of the graph for each of these examples?
$endgroup$
– MPW
Sep 16 '14 at 2:25
$begingroup$
Honestly, no. Please explain
$endgroup$
– Kissamer
Sep 16 '14 at 2:34
$begingroup$
I just posted an answer/hint. Please read it and let me know if you can understand what I mean.
$endgroup$
– MPW
Sep 16 '14 at 2:36
$begingroup$
Ok, so the values would would be substituted in c in f(x) = (x-c)^2?
$endgroup$
– Kissamer
Sep 16 '14 at 2:56
1
$begingroup$
Each value of $c$ defines a different function, and each one has a different graph. The graphs are all similar, but somewhat different. The point of the problem is for you to understand how the particular form makes the functions graph change as $c$ changes. In every case, the graph is a parabola, but in (1) the various parabolas are shifted horizontally by $c$ units, and in (2) the parabolas are stretched vertically by a factor of $c$. Fix the given value of $c$, make a table for $x$-values in $[-5,5]$, and plot the points. You should see it.
$endgroup$
– MPW
Sep 16 '14 at 4:57