Chapter 3: Q 358. (page 344)

a) Graph each function. b) State its domain and range. Write the domain and range in interval notation.
$f (x) = 2 x^{2} .$

Short Answer

Expert verified

Domain of the given function is $(- \infty, \infty) .$ Range of the function is $[0, \infty) .$

Step by step solution

Step 1. Given Information

Given function are $f (x) = 2 x^{2} .$

Step 2. Linear function

It is not a linear function. Create the values using x-values. It can form ordered pairs. Connect and plot them to form graph.

$x$	$y = f (x)$	$(x, y)$
$0$	$y = 2 {(0)}^{2} \to y = 0$	$(0, 0) .$
$- 1$	$y = 2 {(- 1)}^{2} \to y = 2$	$(- 1, 2)$
$1$	$y = 2 {(1)}^{2} \to y = 2$	$(1, 2)$
$- 2$	$y = 2 {(- 2)}^{2} \to y = 8$	$(- 2, 8)$
$2$	$y = 2 {(2)}^{2} \to y = 8$	$(2, 8)$

Step 3. Graph of the function

The graph of the function can be drawn as,

Step 4. Domain and Range

Given function is a quadratic function, domain of quadratic function is all real numbers. Domain of the function is $(- \infty, \infty) .$ Given function is a quadratic function and graph represent the y-positive values, range of given function is all real numbers which is greater than or equal to zero. Range of the function is $[0, \infty) .$

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.

a) Graph each function. b) State its domain and range. Write the domain and range in interval notation.
$f (x) = 2 x^{2} .$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Linear function

Step 3. Graph of the function

Step 4. Domain and Range

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Mechanics Maths

Logic and Functions

Applied Mathematics

Theoretical and Mathematical Physics

Decision Maths

Study anywhere. Anytime. Across all devices.

a) Graph each function. b) State its domain and range. Write the domain and range in interval notation.f(x)=2x2.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Linear function

Step 3. Graph of the function

Step 4. Domain and Range

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Mechanics Maths

Logic and Functions

Applied Mathematics

Theoretical and Mathematical Physics

Decision Maths

Study anywhere. Anytime. Across all devices.

a) Graph each function. b) State its domain and range. Write the domain and range in interval notation.
$f (x) = 2 x^{2} .$