Aleks - Aline Maceno Weis - 3.2 Daily Problems 1 PDF

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7/14/2021

ALEKS

SAMPLE QUESTION Use the function below to answer the following questions. x

f x =3 +4 (a) Use transformations of the graph of

y=3

x

to graph the given function.

(b) Write the domain and range in interval notation. (c) Write an equation of the asymptote. EXPLANATION

(a) Use transformations of the graph of

y=3

x

to graph the given function.

x

f x =3 +4 The graph of

f is the graph of the parent function y = 3

x

shifted

4units upward.

x The parent function y = 3 is an increasing exponential function. We can plot a few points on the graph of and use these points and the horizontal asymptote to form the outline of the transformed graph.

x

y=3

−2

1 9

−1

1 3

0

1

1

3

2

9

Shift the graph of

y=3

x

x

y=3

x

up

4 units. For example, the point 0, 1

Notice that with the vertical shift, the new horizontal asymptote is

y=3 y = 4.

on

x

corresponds to

0, 5

on

x

f x = 3 + 4.

y 10

x

8

f x = 3

x

y =3

6

+

4 4

y= 4

2 x -4

-3

-2

-1

1

2

3

4

-2 -4

https://www-awu.aleks.com/alekscgi/x/Isl.exe/1o_u-IgNsIkr7j8P3jH-lBhBKpIvJLUg6NO6tj9qFltz6nQLOPsPMGhYOBlWBnZyMTAdO_SB_Zt2yTVHbAJ… 1/3

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ALEKS -6 -8 -10

Thus, the graph of

x

f x = 3 + 4 is: y 10 8 6 4 2 x

-4

-3

-2

-1

1

2

3

4

-2 -4 -6 -8 -10

(b) Write the domain and range in interval notation. The domain of the function

f is − ∞, ∞ . The range of the function fis 4, ∞

.

(c) Write an equation of the asymptote. The equation of the horizontal asymptote is

y = 4.

ANSWER

Part 1 of 3

https://www-awu.aleks.com/alekscgi/x/Isl.exe/1o_u-IgNsIkr7j8P3jH-lBhBKpIvJLUg6NO6tj9qFltz6nQLOPsPMGhYOBlWBnZyMTAdO_SB_Zt2yTVHbAJ… 2/3

7/14/2021

ALEKS 14 13 12 11 10 9 8 7 6 5 4 3 2 1

y

x

-9 -8 -7 -6 -5 -4 -3 -2 -1-1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11 -12 -13 -14

1

2

3

4

5

6

7

8

9

Part 2 of 3

The domain of the function The range of the function

f is − ∞, ∞ .

f is 4, ∞ .

Part 3 of 3

The equation of the horizontal asymptote is

y = 4.

https://www-awu.aleks.com/alekscgi/x/Isl.exe/1o_u-IgNsIkr7j8P3jH-lBhBKpIvJLUg6NO6tj9qFltz6nQLOPsPMGhYOBlWBnZyMTAdO_SB_Zt2yTVHbAJ… 3/3...