Chapter 9: Q46. (page 595)

Graph each function. Find the $y$ -intercept, and state the domain and range.
$y = 3^{x} + 1$

Short Answer

Expert verified

The graph of the function is:

$y$ -intercept is $(0, 2)$ and domain is all real number and range is $y > 1$ .

Step by step solution

Step 1. Graph the equation.

Graph of the function: $y = 3^{x} + 1$

Step 2. Find the y-intercept.

The $y$ -intercept of a graph is the point where the graph intersects the $y$ -axis that is., $x$ -coordinate of a $y$ -intercept is 0. So, to find $y$ -intercept substitute 0 for $x$ into the equation.

$y = 3^{x} + 1$

role="math" localid="1647766929721" $\begin{array}{l} y = 3^{x} + 1 \\ = 3^{0} + 1 [x = 0] \\ = 1 + 1 \\ = 2 \end{array}$

Thus, $y$ –intercept is $y = 2$ .

Step 3. Find the range and domain.

The domain of a function $f (x)$ is the set of all values for which the function is defined, and the range of the function is the set of all values that $f$ takes.

From the graph, it can be concluded that domain is all real number and range is $y > 1$ .

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Graph each function. Find the $y$ -intercept, and state the domain and range.
$y = 3^{x} + 1$

Short Answer

Step by step solution

Step 1. Graph the equation.

Step 2. Find the y-intercept.

Step 3. Find the range and domain.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Pure Maths

Theoretical and Mathematical Physics

Calculus

Geometry

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Graph each function. Find the y-intercept, and state the domain and range.y=3x+1

Short Answer

Step by step solution

Step 1. Graph the equation.

Step 2. Find the y-intercept.

Step 3. Find the range and domain.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Pure Maths

Theoretical and Mathematical Physics

Calculus

Geometry

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Graph each function. Find the $y$ -intercept, and state the domain and range.
$y = 3^{x} + 1$