Chapter 13: Q. 6 (page 870)

Graph $g (x) = 3^{x - 1} + 5$ using transformations. Determine the domain, the range, and horizontal asymptote of $g$ .

Short Answer

Expert verified

The graph of the function:

Step by step solution

Step 1. Given information.

The function to be plotted is:

$g (x) = 3^{x - 1} + 5$

Step 2. The graph of y=3x.

$y = 3^{x}$

When $x = 0$ , then

x	y	(x, y)
0	1	(0,1)
1	3	(1,3)
-1	$\frac{1}{3}$	localid="1647756706009" $(- 1, \frac{1}{3})$
-3	$\frac{1}{27}$	localid="1647756712423" $(- 3, \frac{1}{27})$

Locate these points in the coordinate plane and match all points then extend the graph.

Step 3. To draw graph of y=3x-1

Horizontally shift the above graph by 1 unit towards right.

Step 4. To graph g(x)=3x-1+5

Vertically shift the above graph by 5 units upwards.

From this graph we can see that as $x \to - \infty$

$g (x) \to 5$

So, the horizontal asymptote of the function is:

$y = 5$ .

Step 5. To find the domain and the range of the function.

From the above graph we can see that values of $x$ is $(- \infty, \infty)$ .

The value of the $y$ is $(5, \infty)$ .

So the domain is : $(- \infty, \infty)$ .

The range is: $(5, \infty)$ .

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Graph $g (x) = 3^{x - 1} + 5$ using transformations. Determine the domain, the range, and horizontal asymptote of $g$ .

Short Answer

Step by step solution

Step 1. Given information.

Step 2. The graph of y=3x.

Step 3. To draw graph of y=3x-1

Step 4. To graph g(x)=3x-1+5

Step 5. To find the domain and the range of the function.

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Graph g(x)=3x-1+5 using transformations. Determine the domain, the range, and horizontal asymptote of g.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. The graph of y=3x.

Step 3. To draw graph of y=3x-1

Step 4. To graph g(x)=3x-1+5

Step 5. To find the domain and the range of the function.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Geometry

Mechanics Maths

Decision Maths

Applied Mathematics

Statistics

Study anywhere. Anytime. Across all devices.

Graph $g (x) = 3^{x - 1} + 5$ using transformations. Determine the domain, the range, and horizontal asymptote of $g$ .