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....