What are the domain and range of the function f(x) = 3x + 5?

Asked by maham237 @ 28/11/2020 in Mathematics viewed by 363 People

Answered by maham237 @ 28/11/2020

The domain is the set of all real numbers, i.e.,

-∞ < x < ∞ or x ∈ (-∞, ∞) or x ∈ R.

The range is the set of all real numbers, i.e.,

-∞ < y < ∞ or y ∈ (-∞, ∞) or y ∈ R.

Further explanation

The domain of a function is the set of all values that can be plugged into a function and have the function defined. Besides that, the function has a real number for a value.

Given the function f(x) = 3x + 5. This function is a line function, that is, the simplest polynomial function. The polynomial functions have any real number as their domain.

In our problem, there are no restrictions on the domain (x value). Therefore, this line is continuous for all real values of x.

Hence, in all notations, the domain is the set of all real numbers, i.e.,

$\boxed{ \ -\infty < x < \infty \ }$ , or
$\boxed{ \ x \ \epsilon \ (-\infty, \infty) \ }$ , or
$\boxed{ \ x \ \epsilon \ R \ }$

The range of a function is the set of all possible values that a function can take.

This is a line with a slope is 3, so this is not a horizontal line that has a fixed value.

Hence, in all notations, the range is the set of all real numbers, i.e.,

$\boxed{ \ -\infty < y < \infty \ }$ , or
$\boxed{ \ y \ \epsilon \ (-\infty, \infty) \ }$ , or
$\boxed{ \ y \ \epsilon \ R \ }$

Learn more

The range of the given function brainly.com/question/1435353
Determine the domain of the composite function brainly.com/question/3852778
If f(x) = x² – 2x and g(x) = 6x + 4, for which value of x does (f o g)(x) = 0? brainly.com/question/1774827

Keywords: what are, the domain and range, the function f(x) = 3x + 5, all real numbers, line, slope, defined

What are the x-intercepts of the function f(x) = –2x2 – 3x + 20?

Asked by maham237 @ 26/12/2020 in Mathematics viewed by 321 persons

What are the x-intercepts of the function f(x) = –2x2 – 3x + 20? (–4, 0) and and (4, 0) (–5, 0) and (2, 0) (–2, 0) and (5, 0)

For the function f(x) = (x − 2)2 + 4, identify the vertex, domain, and range.

Asked by maham237 @ 25/12/2020 in Mathematics viewed by 311 persons

For the function f(x) = –(x + 1)2 + 4, identify the vertex, domain, and range.

Asked by maham237 @ 22/12/2020 in Mathematics viewed by 321 persons

For the function f(x) = –(x 1)^2 + 4, identify the vertex, domain, and range. a. The vertex is (–1, 4), the domain is all real numbers, and the range …

What are the domain and range of f(x) = 2(3x)?

Asked by maham237 @ 22/12/2020 in Mathematics viewed by 283 persons

What are the domain and range of f(x) = 2(3x)? A. domain (-infinity, infinity), range (0,infinity) B. domain (-infinity,infinity) range (2,infinity) C. domain (0,infinity),range (-infinity,infinity)D.domain (2,infinity) range (-infinity.infinity)

The range of the function f(k) = k2 + 2k + 1 is {25, 64}. what is the function’s domain?

Asked by maham237 @ 24/12/2020 in Mathematics viewed by 301 persons

{5, 8} {-5, -8} {3, 8} {4, 7} {4, 8}

Which graph represents the function f(x) = (x – 5)2 + 3?

Asked by wiki @ 07/11/2020 in Mathematics viewed by 363 persons

What are the domain, range, and asymptote of h(x) = (1.4)x + 5?

Asked by maham237 @ 25/12/2020 in Mathematics viewed by 346 persons

What are the domain, range, and asymptote of h(x) = (1.4)^x + 5? A. domain: {x | x is a real number}; range: {y | y > 5}; asymptote: y = …

If f(x) = x2 – 25 and g(x) = x – 5, what is the domain of mc006-1.jpg?

Asked by maham237 @ 25/12/2020 in Mathematics viewed by 372 persons

If f(x) = x2 – 25 and g(x) = x – 5, what is the domain of mc006-1.jpg? all real values of x all real values of x except x …

Let f(x)= 3x – 6 and g(x) = x –2. find f/g and its domain.

Asked by maham237 @ 22/12/2020 in Mathematics viewed by 325 persons

Given the parent functions f(x) = log10 x and g(x) = 3x − 1, what is f(x) • g(x)?

Asked by maham237 @ 25/12/2020 in Mathematics viewed by 436 persons

Given the parent functions f(x) = log10 x and g(x) = 3x - 1, what is f(x) g(x)? f(x) g(x) = log10 (3x - 1)x f(x) g(x) = log10 x3x …

The graph of which function has a minimum located at (4, –3)?f(x) = x2 + 4x – 11 f(x) = –2x2 + 16x – 35 f(x) = x2 – 4x + 5 f(x) = 2x2 – 16x + 35

Asked by maham237 @ 27/12/2020 in Mathematics viewed by 692 persons

Given the parent functions f(x) = 5x − 1 and g(x) = 3x − 9, what is g(x) − f(x)?

Asked by maham237 @ 22/12/2020 in Mathematics viewed by 422 persons

Given the parent functions f(x) = 5x − 1 and g(x) = 3x − 9, what is g(x) − f(x)? g(x) − f(x) = 3x − 8 − 5x g(x) …

How to describe the domain and range of a function

Asked by admin @ 07/11/2021 in Mathematics viewed by 427 persons

Inequalities that Describe Domain and Range: Complete the inequality below to describe the domain of the graph shown. Domain: __ is less than x which is less than or equal …