Questions: Graph the logarithmic function. g(x) = 4 log2 x Plot two points on the graph of the function, and also draw the asymptote. Then click on the graph-a-function button.

Graph the logarithmic function. g(x) = 4 log2 x Plot two points on the graph of the function, and also draw the asymptote. Then click on the graph-a-function button.
Transcript text: Graph the logarithmic function. \[ g(x)=4 \log _{2} x \] Plot two points on the graph of the function, and also draw the asymptote. Then click on the graph-a-function button.
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Solution

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Solution Steps

Step 1: Find two points on the graph

We need to find two points that satisfy the equation _g(x) = 4log₂x_.

  • Point 1: Let _x = 1_. Then _g(1) = 4log₂(1) = 4 * 0 = 0_. So, the first point is (1, 0).

  • Point 2: Let _x = 2_. Then _g(2) = 4log₂(2) = 4 * 1 = 4_. So, the second point is (2, 4).

Step 2: Identify the asymptote

Logarithmic functions of the form _logₙ x_ have a vertical asymptote at _x = 0_. This holds true for multiples of logarithmic functions as well. Thus, the given function _g(x)_ has a vertical asymptote at _x = 0_.

Step 3: Plot points and draw graph

Plot the two points (1,0) and (2,4) on the graph. Draw a vertical asymptote at x=0. Sketch a logarithmic curve which passes through these two points and approaches, but doesn't cross, the vertical asymptote.

Final Answer:

The graph of the function _g(x) = 4log₂x_ passes through the points (1, 0) and (2, 4). It has a vertical asymptote at _x = 0_. A sketch of the graph is increasing from left to right as it moves away from the asymptote.

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