Question

Below is the graph of f(x)=2In(x). how would you describe the graph of g(x)=4In(x)

Answer 1

$\bf \qquad \qquad \qquad \qquad \textit{function transformations} \\ \quad \\\\ \begin{array}{rllll} % left side templates f(x)=&{{ A}}({{ B}}x+{{ C}})+{{ D}} \\ \quad \\ y=&{{ A}}({{ B}}x+{{ C}})+{{ D}} \\ \quad \\ f(x)=&{{ A}}\sqrt{{{ B}}x+{{ C}}}+{{ D}} \\ \quad \\ f(x)=&{{ A}}(\mathbb{R})^{{{ B}}x+{{ C}}}+{{ D}} \\ \quad \\ f(x)=&{{ A}} sin\left({{ B }}x+{{ C}} \right)+{{ D}} \end{array}$


$\bf \begin{array}{llll} % right side info \bullet \textit{ stretches or shrinks horizontally by } {{ A}}\cdot {{ B}}\\\\ \bullet \textit{ flips it upside-down if }{{ A}}\textit{ is negative} \\\\ \bullet \textit{ horizontal shift by }\frac{{{ C}}}{{{ B}}}\\ \qquad if\ \frac{{{ C}}}{{{ B}}}\textit{ is negative, to the right}\\\\ \qquad if\ \frac{{{ C}}}{{{ B}}}\textit{ is positive, to the left}\\\\ \end{array}$

$\bf \begin{array}{llll} \bullet \textit{ vertical shift by }{{ D}}\\ \qquad if\ {{ D}}\textit{ is negative, downwards}\\\\ \qquad if\ {{ D}}\textit{ is positive, upwards}\\\\ \bullet \textit{ period of }\frac{2\pi }{{{ B}}} \end{array}$

now... with that template in mind, let's see yours

$\bf \begin{array}{llll} g(x)=&4ln(x)\implies &2(2)ln(x)\\ &\uparrow &\uparrow \\ &A&A \end{array}$

A is twice as large as in f(x), thus the graph shrinks twice as much in g(x)

Answer 2

Answer:

The graph of f(x) vertically stretch by factor 2.

Step-by-step explanation:

The given functions are

$f(x)=2ln(x)$

$g(x)=4ln(x)$

$g(x)=kf(x+b)+c$

Where, k is stretch factor, b is horizontal shift and c is vertical shift.

If k>1, then it represents vertical stretch and if k<1, then it represents vertical compression.

If b>0, then the graph of f(x) shifts b units left and if b<0, then the graph of f(x) shifts b units right.

If c>0, then the graph of f(x) shifts c units up and if c<0, then the graph of f(x) shifts c units down.

$g(x)=2(2ln(x))$

$g(x)=2f(x)$

The stretch factor is 2>0, it means the graph of f(x) vertically stretch by factor 2.