Mathematics, 22.07.2021 17:50 janahiac09

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

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Answer from: mendezmarco2004

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: $(3,\infty)$

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

Answer from: genyjoannerubiera

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.

Answer from: Quest

y-y1=4(x-x1)

step-by-step explanation:

this is point-slope form since you only have 4 as the slope it goes in place of m

hope this : )

Answer from: Quest

answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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