Q 361. a) Graph each function. b) State... [FREE SOLUTION]

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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 3: Q 361. (page 344)

a) Graph each function. b) State its domain and range. Write the domain and range in interval notation.
$f (x) = \frac{1}{2} x^{2} .$

Short Answer

Expert verified

Domain of the function is $(- 鈭�, 鈭�) .$ Range of the function is $[0, 鈭�) .$

Step by step solution

Step 1. Given information

The given function is $f (x) = \frac{1}{2} x^{2}$

Step 2. Formation of ordered pairs

This is not a linear function. The table can be created with different x-values. The ordered pairs can be formation and plot them for graph formation.

$x$	$y = f (x)$	$(x, y)$
$0$	$y = \frac{1}{2} {(0)}^{2} 鈫� y = 0$	$(0, 0)$
$- 1$	$y = \frac{1}{2} {(- 1)}^{2} 鈫� y = \frac{1}{2}$	$(- 1, \frac{1}{2})$
$1$	$y = \frac{1}{2} {(1)}^{2} 鈫� y = \frac{1}{2}$	$(1, \frac{1}{2})$
$- 2$	$y = \frac{1}{2} {(- 2)}^{2} 鈫� y = 2$	$(- 2, 2)$
$2$	$y = \frac{1}{2} {(2)}^{2} 鈫� y = 2$	$(2, 2)$

Step 3. Graph of the function

The graph 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 $(- 鈭�, 鈭�) .$ 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 $[0, 鈭�) .$

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91影视

a) Graph each function. b) State its domain and range. Write the domain and range in interval notation.
$f (x) = \frac{1}{2} x^{2} .$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Formation of ordered pairs

Step 3. Graph of the function

Step 4. Domain and Range

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91影视

a) Graph each function. b) State its domain and range. Write the domain and range in interval notation.f(x)=12x2.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Formation of ordered pairs

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

Discrete Mathematics

Pure Maths

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Theoretical and Mathematical Physics

Geometry

Probability and Statistics

Study anywhere. Anytime. Across all devices.

a) Graph each function. b) State its domain and range. Write the domain and range in interval notation.
$f (x) = \frac{1}{2} x^{2} .$