Mathematics: Graph the function g(x) = 3^x + 3 and give its domain and range using interval notation.

Graph the function g(x) = 3^x + 3 and give its domain

Ответ:

JOEFRESH10

21.08.2021

When a function is plotted on a graph, the domain and the range of the function are the x-coordinate and the y-coordinate respectively.

The domain and the range of the given function are:

Domain: $(-\infty,\infty)$

Range: $(3,\infty)$

The given function is:

g(x) = 3^x + 3

First, we plot the graph of g(x)

To do this, we need to generate values for x and g(x). The table is generated as follows:

$x = 0 \to g(0) = 3^0 + 3 = 4$

$x = 1 \to g(1) = 3^1 + 3 = 6$

$x = 2 \to g(2) = 3^2 + 3 = 12$

$x = 3 \to g(3) = 3^3 + 3 = 30$

$x = 4 \to g(4) = 3^4 + 3 = 84$

The generated values in tabular form are:

$\begin{array}{cccccc}x & {0} & {1} & {2} & {3} & {4} \ \\ g(x) & {4} & {6} & {12} & {30} & {84} \ \end{array}$

Refer to the attached image for graph of g(x)

To determine the domain, we simply observe the x-axis.

The curve stretches through the x-axis, and there are no visible endpoints on the axis. This means that the curve starts from $-\infty$ to $+\infty$

Hence, the domain of the function is: $(-\infty,\infty)$

To determine the range, we simply observe the y-axis.

The curve of g(x) starts at y = 3 on the y-axis and the curve faces upward direction. This means that the curve of g(x) is greater than 3 on the y-axis.

Hence, the range of the function is: $(3,\infty)$

Ответ:

cesarcastellan9

21.08.2021

Mathematics

Function: $g(x) = 3^{x} + 3$ . Domain: $Dom \{g(x)\} = \mathbb{R}$ , Range: $Ran \{g(x) \} = (3, +\infty)$ , respectively.

In Function Theory, the domain of a function f(x) represents the set of values of the independent variable (), whereas the range of the function is the set of values of the dependent variable.

The Domain of the Function represents the set of values of (horizontal axis), whereas the Range it is the set of values of (vertical axis). After analyzing the existence of Asymptotes, we complement with graphic approaches and conclude where domain and range (in Interval notation) are.

Analytically speaking, the domain of exponential functions is the set of all real numbers and the range of g(x) is any number between $\lim_{x \to -\infty} g(x)$ and $\lim_{x \to +\infty} g(x)$ . In a nutshell, we get the following conclusions in interval notation:

Domain: $Dom \{g(x)\} = (-\infty, +\infty)$ , Range: $Ran \{g(x) \} = (3, +\infty)$

Lastly, we proceed to complement this analysis by graphing function with the help of a graphing tool.

According to the image, domain and range coincides with outcomes from analytical approaches.

Graph the function g(x) = 3^x + 3 and give its domain and range using interval notation.

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Ответ:

alexamorantess

04.11.2021

Mathematics

108.41 i pretty sure

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Graph the function g(x) = 3^x + 3 and give its domain and range using interval notation.

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